The 27-year-old is certain to leave Ajax in the transfer window, but his destination has not yet been decided.
Atletico boss Diego Simeone believes the Argentine is a player who can improve his team’s backline.
However, according to Goal it is Frank Lampard’s Chelsea who are best positioned to sign Tagliafico.
The London club have already taken steps to convince Tagliafico and, at the moment, have more money than Atleti.
The player’s agent, Ricardo Schlieper, revealed in May that in addition to Chelsea, PSG had spoken to him.
Atletico serious about Tagliafico
Atleti can’t be ruled out of the race though, and in recent days made contact with Ajax to try and work out a deal.
Simeone is happy with the performances of Renan Lodi but wants another high-level left-back to foster competition in the squad.
Tagliafico is a fan of Atletico’s sporting direction and the coaching staff led by Simeone.
However, within Atletico they know how difficult this deal could be with two wealthy English clubs interesting.
The La Liga side are therefore looking at creative solutions to make a good offer to Ajax.
Argentina star Tagliafico appeared 34 times for Ajax this season, scoring five and assisting seven goals.
He is under contract with the Amsterdam club until 2022 and is valued at around €26m.
Independiente, Tagliafico’s former club, are watching with interest as they have a 15 per cent sell-on clause.