Klopp has led Liverpool to back-to-back Champions League finals but is adamant that their impressive recent track record does not make them the title favourites.
Arsenal manager Arsene Wenger spoke last week of his desire to keep the 24-year-old Oxlade-Chamberlain, who was also a target for champions Chelsea.
Reports in British media put the latest bid at 125 million euros.
While Lyon rallied to hold Leipzig 2-2 after a Memphis Depay strike, it was the English clubs who made a mark on the night. Liverpool and Chelsea moved into the last 16 with contrasting wins and now all four English clubs, including Manchester City and Tottenham Hotspur, are in the Champions League knockouts this season.
Barcelona continued their rampant run of domestic form to beat Osasuna 2-0 away from home on Saturday and move to within two points of La Liga leaders Atletico Madrid, with Lionel Messi setting up goals scored by Jordi Alba and teenager Ilaix Moriba.
Chelsea's Ruben Loftus-Cheek had a Europa League night to remember by scoring the first hat-trick of his career as the midfielder inspired them to a 3-1 home win over Belarus champions BATE Borisov on Thursday.
Napoli brush aside lowly Crotone to go third in Serie A.
IMAGES from the Europa League matches played on Thursday
Images from Sunday's Premier League matches.
Manchester City's quadruple bid remained intact as Ilkay Gundogan and Kevin de Bruyne secured a 2-0 win at Everton in their FA Cup quarter-final clash
Five talking-points from the Premier League weekend after Manchester City suffered a shock home loss to Crystal Palace, meaning that Liverpool stayed four points clear at the top following their win over Wolverhampton Wanderers.
Images from the FIFA World Cup Round of 16 match played between Switzerland and Sweden in St Petersburg on Tuesday
Leaders Manchester City kept up their unbeaten run with a 3-1 win over Bournemouth on Saturday. Manchester United salvaged a 2-2 draw at Southampton, who sacked manager Mark Hughes on Monday.
Bayern Munich edged past Werder Bremen 2-1 on Saturday for a Bundesliga record 13th consecutive win over them to stay three points clear at the top of the table.
Karim Benzema fired Real Madrid to a 1-0 win in the city derby against Atletico Madrid on Saturday which underlined Real's La Liga title credentials. Bayern Munich scored three goals in the opening 26 minutes to defeat Mainz 05 3-1 away on Saturday and go two points clear at the top of the Bundesliga with their sixth straight win.
Twelve months ago Liverpool were ripping up the record books on the way to their first English top-flight title for 30 years but defeat by Everton on Saturday left them mulling a host of far less flattering statistics.
Napoli rediscovered their scoring touch as they brushed aside Inter Milan 3-0 on Friday, sending their opponents' new coach Stefano Pioli back to the drawing-board.
A round of Wednesday night's Champions League group stage matches.
Cristiano Ronaldo scored twice in his 150th European appearance to give Real Madrid a 3-1 victory at Borussia Dortmund, their first against them in Germany, and make it two wins out of two matches in their Champions League Group H.
A round-up of Saturday's football action in La Liga, Bundesliga and Ligue 1.
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field
Images from football matches played across Europe.
Cristiano Ronaldo opened the scoring as Juventus beat visiting Bologna 2-1 on Saturday to move four points clear at the top of the Serie A table. Ronaldo struck from close range after 19 minutes, but Danilo levelled for the visitors soon afterwards.
A round-up of Saturday's matches in Ligue 1, Serie A and Bundesliga.
Arsenal and Chelsea were among seven teams to reach the Europa League knockout stage on Thursday, while last year's runners-up Olympique de Marseille were eliminated at the group phase.
Cristiano Ronaldo helped Juventus continue their unbeaten start to the Serie A season with a comfortable 2-0 home victory over struggling SPAL on Saturday.
News of all that's transpired on and off the football field
Real Madrid's teenage Brazilian duo Vinicius Junior and Rodrygo Goes sent them top of La Liga as both scored in a 2-0 win over Osasuna on Wednesday.
Images from the football matches played across Europe on Sunday.
News of all that's transpired on and off the football field.
The victory moved second-placed Bayern, who take on Celtic in the Champions League next week, up to 17 points, two behind Dortmund who suffered their first home loss in 41 league matches.
News of all that's transpired on and off the football field
National football team goalkeeper Subrata Paul is set to become the first Indian player to join a first division side in Europe as he has been offered a six-month contract by Danish top tier club FC Vestsjaelland.
Barcelona's fourth defeat of the season left them seventh in the standings on 14 points after 10 games, 12 points behind leaders Atletico.
News of all that's transpired on and off the football field
Giacomo Bonaventura's free kick earned Milan a 1-0 win over Pescara to move them into the top three of Serie A on Sunday.
Manchester City failed in an audacious transfer deadline day move for Leicester City midfielder Riyadh Mahrez, British media reported on Wednesday.
News of all that's transpired on and off the football field
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