Spurs boss Mauricio Pochettino has cooled suggestions he will look to strengthen his ranks before the end of the month, but that is not stopping reports linking him with a swoop for Gaitan.
The 28-year-old has struggled to make an impact at Atletico after joining them from Benfica, leading to reports a fresh start elsewhere could be on the cards.
It has been suggested a loan deal at White Hart Lane for the remainder of the season could be an option, but Spanish football expert Guillem Balague says that is unlikely.
“It is very difficult to adapt to Simeone's Atletico Madrid,” said Balague. “A lot of players haven't been able to do it. They have got a lot of hopes for Gaitan, who keeps going in and out of the side but he has to work much harder with the ball to be able to make an impact.
"At the moment, he is just a super sub, but they don't want him to go in January."