The 24-year-old Atletico Madrid star has caught the Blues’ eye having scored 25 goals so far this season and has been on their radar before.
But instead of waiting a few months and signing him while he was still at Real Sociedad, Chelsea made a blunder and opted for Mohamed Salah.
It’s already going to take a vast sum of money to correct the error, but his eventual signing could mean it’s curtains for the likes of Loic Remy as Chelsea will have to make room in their squad.
They are unlikely to move on the underwhelming Juan Cuadrado after a few months due to the fee it took to bring him to Stamford Bridge.
Remy has not performed badly when given the chance and boasts a decent goals to games ratio, but he has been missing during the crucial moments and does not represent the sort of man that can be relied upon when Diego Costa is unavailable.
At Atletico, Griezmann has helped filled the void left by Costa in terms of goals when he departed Madrid last summer and the hope would be that he’ll again take the burden off the Spanish international at Chelsea, especially as he has shown the ability and versatility to operate anywhere across the front three.
Chelsea’s attack is a little lopsided at the moment as there is no-one on the right-hand side to match Eden Hazard’s brilliance on the left and, in my opinion, Willian is better in a central position than he is on the wings.
If Mourinho is to play more expansive football than he has set his side up to do over the last few months, which you would expect he will, then the prospect of the trio interchanging in the Chelsea attack is mouth watering.
It’s thought Atletico are clambering to get the player to sign a new deal which would increase his buyout fee, so Chelsea would have to move quickly to secure his services.
This could be made easier by the presence of Jorge Mendes, who is acting as an advisor for Griezmann and enjoys a close relationship with Mourinho as his agent.
Despite winning the Premier League title there could be a few changes at Chelsea this summer as they track star names like Griezmann, meaning the likes of Remy, Petr Cech, Filipe Luis and Didier Drogba could all be moved on to make room for a new crop of talent.