The player's agent Jose Iribarren, who told French media publication Foot Mercato that his client would not be staying at Wanda Metropolitano past the closure of the winter window next month.
Gaitan has struggled for regular game time with one of La Liga's biggest hitters this term and will be desperate to feature more often at club level to give himself the best chance of being part of Argentina's squad for next summer's World Cup.
Spurs are the latest Premier League side to be mooted as a potential destination for the 29-year-old, and Iribarren claimed that a number of English clubs are in the running to try and lure Gaitan away from Spain's capital.
He said: "I can tell you English clubs are interested. Yes, he'll undoubtedly leave Atletico in January. He has a lot of concrete offers. Nicolas was an important player when he played in Argentina, at Benfica and with the national team.
"He can't continue in these conditions. If he can't play a string of matches, nor win the coach's trust. A player wants to play. We're going to see with Atletico which solution we can find."
Gaitan is cup-tied and will be 30 in a month. We already have a 32-year old Llorente. Why add another player we will only get rid of in the summer?— Aaron Pitters (@aaronpitters) December 22, 2017
Cynics among the footballing fanbase will look at Iribarren's comments and suggest that he is merely drumming up interest in his client - who has been fruitlessly linked to United for several seasons now - for his own financial gain.
However, others will assume that Gaitan could very well be on his way to Spurs' temporary home Wembley after the turn of the year, and he would arguably get a decent amount of starts in north London under compatriot Mauricio Pochettino.
The Tottenham boss is on the lookout for attacking reinforcements in January to strengthen his options out wide and securing the signature of the former Benfica and Boca Juniors star could be high on his wish list.
Gaitan has only featured 12 times for Atletico this season, with only four of those appearances coming from the start under Diego Simeone.