Griezmann was believed to be Man United's leading transfer target for this summer's window, but it has been claimed that the Frenchman is no longer a priority as Red Devils boss Jose Mourinho looks to sign a specialist centre-forward.
Zlatan Ibrahimovic's future at Old Trafford is still up in the air, although it does appear that the Swede will not sign the 12-month extension that was placed on the table before he picked up a season-ending knee injury.
Lacazette, meanwhile, appeared to be heading for Atletico this summer as a replacement for Griezmann, but the Madrid outfit have lost their appeal relating to a transfer ban and will therefore be unable to sign new players in this transfer window.
According to The Mirror, that has led Mourinho, who is currently on holiday, to turn his attention to Lacazette, who is also believed to be a target for Arsenal and Liverpool ahead of the 2016-17 campaign.
The 26-year-old, said to be rated at £50m, scored 37 goals in 45 appearances for Lyon last season, and has now managed 129 goals in 275 appearances since making the breakthrough into the first team during the 2009-10 season.
Earlier this year, Lacazette revealed that he was ready to leave Lyon in this summer's transfer window.