Vicente Rodriguez scored in the 81st-minute to give Valencia a 3-2 victory over Real Madrid in the first leg of the Spanish Supercup.
Manchester United's miserable season continued with a 3-2 home defeat by Galatasaray.
Real Madrid have courted Mbappe in the past but failed to land the 24-year-old, who signed a contract extension with PSG in May last year.
Atletico Madrid extended their unbeaten run in LaLiga to nine matches with a 2-0 victory over hosts Real Betis on Monday.
Real Madrid are considering creating a subsidiary that would allow external investors to buy a stake of around 5% in the world's most valuable football club.
Real Madrid denied a report that they have offered a world-record 310 million euros (274.65 million pounds) for Paris Saint-Germain (PSG) forward Neymar.
Karim Benzema scored twice in the final few minutes to give Real Madrid a 3-1 win at Espanyol, while Barcelona breezed past Real Valladolid with a comfortable 4-0 LaLiga victory.
Real Madrid's director of football Benito Floro has proposed the club buy Liverpool's Steven Gerrard and Inter Milan's Adriano.
The nine-times European champions finished second on goal difference in Group H of the Champions League behind Juventus, who were held 0-0 at home by BATE Borisov.
Real Madrid's miserable run of results continued as they slid to a shock 1-0 La Liga defeat at Alaves by conceding a goal deep in stoppage time on Saturday, marking their longest run without scoring in over 33 years.
La Liga leaders Real Madrid cruised to a 4-0 home win over relegation-threatened Celta Vigo on Sunday to restore their seven-point lead at the top of the table with a dominant display.
Real Madrid restored their four-point lead over second-placed Barcelona with a 2-0 win against Osasuna in the Spanish Primera Liga.
Double strikes by Thierry Henry and Lionel Messi powered a rampant Barcelona to a 6-2 thrashing of champions Real Madrid in a spectacular Primera Liga clash.
A Dani Carvajal strike in the ninth-minute of stoppage time rescued Real Madrid, earning them a 3-2 comeback win at home against bottom side Almeria on Sunday in a frantic LaLiga tussle that was marked by VAR controversy.
Uruguayan midfielder Fabian Canobbio scored a contentious goal to give promoted Celta Vigo a 3-2 win.
Real Madrid President Florentino Perez has vowed that his club will make a splash in this summer's transfer market.
Real Madrid captain Sergio Ramos performed another rescue act to wreck Napoli's brave comeback attempt and take the Champions League title-holders into the quarter-finals.
Holders Real Madrid will play 2021 winners Chelsea in the Champions League quarter-finals while Manchester City's Pep Guardiola will visit his former club Bayern Munich.
Real Madrid's Brazilian contingent overwhelmed Real Mallorca 4-0 to help move the team up to third in the Primera Liga.
The Spanish giants drew 1-1 at home to Bayer Leverkusen in the Champions League.
Novak Djokovic and Eileen Gu will co-host this year's Laureus World Sports Awards in Madrid, marking a historic first for the prestigious event.
Real Madrid on top because of performances, not referees, says coach Zidane.
Real were pushing hard for the victory they needed to move back on top of the Primera Liga standings.
Images from the UEFA Champions League matches played on Tuesday.
Here, Reuters Sport highlights five reasons why last season's double winners have collapsed.
Real Madrid forward Cristiano Ronaldo wants to leave the club and Spain after being accused of committing tax fraud in the country, a report in Portuguese sports daily A Bola said on Friday.
The victory sent Valencia to the top of the Spanish league.
Portugal star striker Cristiano Ronaldo, who has been out of action since injuring his knee in the successful Euro 2016 final, has vowed to return soon after stepping up training at Real Madrid's Valdebebas training base.
Real Madrid defender Marcelo says the club needed new direction after stuttering under Rafael Benitez and has praised Zinedine Zidane for 'breathing life back' into the team since taking over as coach in January.
A summary of Tuesday's first leg quarter-final action in the UEFA Champions League.
Spanish and French media reported on Tuesday that Real Madrid had made a 160-million-euro ($187.81-million) bid for the 22-year-old World Cup winner, who scored 42 goals in all competitions for PSG last season and has reportedly said he wants to move to Spain.
A first-half penalty earned Lille a shock 1-0 home victory over holders Real Madrid in the Champions League group phase on Wednesday.
Ramos's contract runs out at the end of June and there are only four La Liga games remaining this season.