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After being frozen out at Barcelona, the Uruguayan striker remained in La Liga by signing for Atletico Madrid in a £5.5 million move, where's he scored 19 goals in 26 league appearances.
Top of the table by one point after 29 games, Los Rojiblancos are pushing for a first league title since 2014 under Diego Simeone.
But Todofichajes are reporting that the 34-year-old has a "difficult" relationship with the Argentine manager. It's said that he has become "physically drained" with Simeone's style of football.
Playing extremely conservatively on their way to a 3-0 aggregate loss, Suarez was largely anonymous.
In the second leg at Stamford Bridge, Suarez touched the ball just 19 times and completed six passes during 59 minutes on the pitch.
Upon signing for Atletico, a clause was inserted in his contract allowing him to leave the Wanda Metropolitano in the summer of 2021 without any intervention necessary.
The report from Spain says that Suarez would consider a second stint at Liverpool, where he was a firm fans' favourite after joining from Ajax in 2011.
In total, he scored 82 times in 133 appearances, including 69 in the Premier League, before Barcelona paid £65 million to bring him to the Camp Nou.
Luis Suarez is the best footballer to ever play for Liverpool Football Club. https://t.co/UzRTtQngw8- Terry (@tzrry) April 8, 2021
Last month, there was some talk that the potential sale of talisman Mo Salah would 'facilitate the arrival' of Suarez at Anfield.
Inter Miami, David Beckham's MLS franchise, are also an option for Suarez in his final years as a professional.
The club made an offer to him in 2020 but he ended up staying in Spain - leading to Gonzalo Higuain joining as a designated player.
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