That embargo expires in January, when Atletico will welcome Diego Costa into their squad amongst others, although any deal for Griezmann is expected to wait until the summer.
He has done little to quieten those rumours in recent times and will have stoked speculation further by making remarks to TF1's 'Telefoot' program that suggest that he would be delighted to join up with the Ligue 1 leaders.
When asked whether he spoke to United boss Mourinho - who is a huge admirer of the France international - on the phone regularly, Griezmann answered: 'No'.
The Portuguese reportedly only has eyes for Bale who is having a torrid time with injuries at the Bernabeu.
Griezmann was previously heavily linked to Manchester United in the summer, with the French superstar even going on to rate his chances of joining the Red Devils as '6 out of 10' in a television interview.
City have also made a "substantial offer" for PSG midfielder Claudio Gomes, with L'Equipe claiming that the player has yet to respond. However, Atletico's transfer ban meant that the 26-year-old forward decided to stay with the club.
West Ham are putting into place plans to make David Moyes' first signing since replacing Slaven Bilic as manager at the London Stadium. That would leave Barcelona to pay the clause.
But he now appears to have poured cold water over the idea of a move to Old Trafford.