Atletico Madrid suffered a first defeat in 13 games in all competitions as they lost 1-0 at home to Villarreal on Tuesday after a late strike from substitute Roberto Soriano.
British media said United had closed on a deal worth up to 70 million euros for Casemiro, who has 63 caps for Brazil.
Lionel Messi hit four goals for leaders Barcelona and Cristiano Ronaldo grabbed a hat-trick for Real Madrid as the two teams warmed up for their midweek King's Cup semi-final clash with crushing La Liga victories on Sunday.
Sevilla maintained their incredible record in the competition after an otherwise difficult season.
Barcelona leapfrogged Atletico Madrid to go top of La Liga after Lionel Messi's acrobatic volley secured a hard-fought 2-1 victory against tenacious Malaga on Saturday.
An unconvincing Real Madrid needed a controversial Cristiano Ronaldo penalty deep into stoppage time to snatch a 2-1 win at promoted Elche on Wednesday that kept them hard on the heels of La Liga leaders Barcelona and Atletico Madrid.
Barcelona extended their winning start to their title defence to six games when Neymar scored his debut La Liga goal and Lionel Messi netted his seventh of the season in an entertaining 4-1 victory at home to Real Sociedad on Tuesday.
Sevilla became surprise Liga leaders on Sunday after beating visiting Celta Viga 2-1 while champions Barcelona drew 1-1 at Valencia thanks to another Lionel Messi strike but are still without a victory in their last four league games.
Atletico Madrid's Jackson Martinez scored his first goal for the club when he came off the bench and curled in a superb effort to seal a hard-fought 3-0 victory at Sevilla in La Liga on Sunday.
Leaders Barcelona survived red cards for Gerard Pique and Rafael Marquez to complete a 2-1 victory over Getafe in La Liga on Saturday while Real Madrid kept pace with a 3-0 win at home to Espanyol.
Chelsea won their first competitive match under coach Mauricio Pochettino with a 3-0 home victory over Premier League new boys Luton Town.
Villarreal's slide continued as a Diego Castro header gave Getafe a 1-1 draw in La Liga on Sunday but the match was overshadowed by a serious injury to Mateo Musacchio.
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Barcelona forward Ousmane Dembele scored twice and produced a mesmerising display to fire his side to a 5-1 win over Villarreal on Wednesday which stretched the champions' unbeaten run this season to 36 games with two remaining.
Sevilla secured third place in the Primera Liga and automatic qualification for the Champions League when a last-minute header from Diego Perotti earned them a 1-0 home win over Deportivo Coruna on Saturday.
Midfielder Dani Ceballos added: "It looks like us changing our coach worked. We have recovered some sensations we had lost and we have got the three points. Now our objective is to win all the games left and finish the season as well as possible."
Real Madrid will go into next weekend's La Liga El Clasico at Barcelona eight points behind their great rivals after Cristiano Ronaldo netted a hat-trick in a 5-1 comeback win at home to promoted Deportivo Coruna on Sunday.
Lionel Messi marked his 300th La Liga appearance with a record-equalling hat-trick and an assist for Neymar as Barcelona stayed hard on the heels of leaders Real Madrid with a 5-0 romp at home to Levante on Sunday.
Barcelona twice came from behind to rescue a point in a 2-2 draw at Valencia while Real Madrid dropped points again in a goalless affair at Racing Santander in La Liga on Wednesday.
Atletico Madrid extended their dominance over neighbours Real with a 1-0 derby win on Saturday that leaves the Bernabeu team virtually out of the Liga title race.
Real Madrid opened a two-point lead over Villarreal at the top of La Liga when Cristiano Ronaldo set a club scoring record in a 3-0 stroll at home to Levante on Saturday.
The home side spurned two chances to extend their advantage before the break but Barca levelled in the 52nd minute when Luis Suarez glanced in Lionel Messi's free kick.
Atletico Madrid have been unable to repeat the magnificent achievements of last season in this campaign but can congratulate themselves on a job well done if they secure a lucrative Champions League berth on Saturday.
Barcelona and Real Madrid both drew away against sides battling relegation in La Liga on Saturday as the top two focused their attentions on next week's Champions League quarter-finals.
Real Madrid extended their unbeaten run to 25 matches and rejoined Barcelona and Atletico Madrid at the top of La Liga when Jese, Karim Benzema and Luka Modric scored in a 3-0 win at Getafe on Sunday.
Real Madrid brushed off the absence of Cristiano Ronaldo and Gareth Bale to beat Espanyol 2-0 away and maintain their 100 per cent start to the league season while matching the La Liga record of 16 consecutive victories.
Real Madrid followed up Tuesday's Champions League success at Manchester United by climbing above beaten city rivals Atletico into second in La Liga when Cristiano Ronaldo struck twice in a 2-1 win at second-bottom Celta Vigo on Sunday.
Lionel Messi netted the 400th goal of his storied career on Saturday as Barcelona trounced Granada 6-0 to maintain the pace at the top of La Liga.
A red hot Luis Suarez scored four goals and contributed three assists as Barcelona's stuttering La Liga title charge sparked back to life with a spectacular 8-0 thrashing of Deportivo La Coruna on Wednesday.
Photos from the La Liga matches played on Sunday
Rodrygo and new recruit Jude Bellingham scored first-half goals to give Real Madrid a 2-0 win at Athletic Bilbao to kick off their LaLiga season.
'We will see, we want to win but at the same time, there are a lot of questions that we need answers to. But in the Asia Cup, I want to see some of the guys batting under pressure against quality teams.'
Real Madrid's early-season woes deepened when they lost 2-1 at home to La Liga champions Atletico Madrid, while substitute Neymar struck twice in Barcelona's 2-0 win against visiting Athletic Bilbao on Saturday.
Barca's second-half stamina key to their massive lead in the standings this season
Atletico Madrid cruised to a 3-0 home win over Real Sociedad on Tuesday to close the gap behind La Liga leaders Barcelona to five points.
Reaching the King's Cup final is of even greater importance than usual for Real Madrid following a demoralising setback in La Liga.
Lionel Messi scored in his 12th consecutive La Liga game to help leaders Barcelona earn a 1-1 draw at Valencia, allowing second-placed Atletico Madrid to close to within nine points after a 1-0 win over Real Betis on Sunday.
Real Madrid forward Cristiano Ronaldo aggravated a leg muscle injury in Saturday's 2-1 win over city rivals Atletico, the La Liga club said.
Lionel Messi created a goal and scored another as Barcelona came from behind to beat struggling Rayo Vallecano 3-1 at home on Saturday and stay seven points clear at the top of La Liga.
Real Madrid strikers Karim Benzema and Gonzalo Higuain are doubts for the trip to play Levante in La Liga on Sunday, a ground that has proved an uncomfortable venue for Jose Mourinho's side over the last two seasons.