Record claims that the Premier League outfit dispatched a scout to observe the Argentine in Benfica's 2-0 victory against Santa Clara on Wednesday in the League Cup.
Gaitan has been strongly linked with a new challenge after an impressive start to his second season at the Estadio da Luz.
Manchester United are also tracking the 23-year-old, with manager Sir Alex Ferguson confessing that he is a fan of the former Boca Juniors star.
However, Gaitan's agent stressed last month that he was unaware of any talks between Benfica and the Red Devils over the transfer of his client.
Gaitan, who joined Benfica in 2010, has a €45 million release clause attached to his contract, which expires in 2016.
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.