Express Sport understands Griezmann was Manchester United's top transfer target for the summer.
But, with Atletico Madrid banned from signing players until January, the Red Devils face a battle to prise him away from Diego Simeone's side.
They have now turned their attentions to Romelu Lukaku after Griezmann all but confirmed he would stay at the La Liga giants – though the Belgium international looks likely to move to Chelsea.
Lacazette, an international team-mate of the Atletico star, had been linked with a move to the Spanish capital to fill the void left by his potential departure.
What Antoine Griezmann has said about his future Sun, June 4, 2017
What has Manchester United target Antoine Griezmann said about his future?
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Speaking to French broadcaster Telefoot in June…
Manchester United are desperate to seal the transfer of Antoine Griezmann
This is a case that can not be ruled out
And the Lyon hotshot has hinted he could still yet sign for them before August, in a move that could pave the way for Griezmann to move to Old Trafford.
"It is possible. This is a case that can not be ruled out," he said.
"I did not think about it too much because the president [of Lyon, Jean-Michel Aulas] said it was not possible.
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Alexandre Lacazette has given Manchester United fresh hope in their Antoine Griezmann pursuit
"We must prepare for all the contingencies but that is not the plan I would prefer."
Liverpool are keen to bring Lacazette to Anfield after a season that saw the France international score 37 goals from 45 games across all competitions.
And he can further endear himself to possible suitors if he lines up for France in a friendly against Sweden on Friday.