The North London outfit, as well as Manchester United, were registered with an interest in the Argentine earlier this year.
Gaitan has found it difficult trying to cement a place in the first team having started just six La Liga games this season.
The midfielder’s agent Jose Iribarren has told Foot Mercato that a number of English clubs are interested in his client, who intends to move on next month.
“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.”
The 29-year-old has been at the Spanish outfit since 2016 when he made the switch from Benfica, where he made more than 250 appearances.
The Premier League club may not necessarily be crying out for Gaitan, but he is certainly capable of providing the team with some attacking flair.
So far, Mauricio Pochettino has been reliant on Christian Eriksen and Dele Alli to lead the way from midfield.
However, both players have experienced dips in form in recent weeks, which could be down to the amount of games they are feating in.
Gaitan would be a decent player to call upon for an injection of quality, plus the midfielder has Champions League experience.
The fact that the player’s agent has confirmed his client has a desire to move in January, puts Tottenham in a good position in terms of negotiations.