The report claims Manchester City have registered their interest in the Real Sociedad winger, joining the likes of PSG, Liverpool, Arsenal, United and Chelsea.
The battle to land the talented French winger seems to be heating up as he continues to impress for his Spanish club in La Liga.
Griezmann found the net again against Barcelona at the weekend, taking his tally for the season to 20 in all competitions.
City already have a number of options in wide positions, not least Jesus Navas, James Milner, David Silva and Samir Nasri. But it's reported that Manuel Pellegrini now has his eye on Griezmann.
The Frenchman has been tipped to make France's World Cup squad for the tournament this summer, despite the fact he's yet to make an appearance for the senior team.
Chelsea, Manchester United and Arsenal were linked with the winger during the January transfer window. But following reports of interest from big-spending French giants PSG, City are now interested as well.