In the summer, United pursued the French forward but a move failed to materialise.
Griezmann said there was a six out of ten chance he would leave for Old Trafford but after a transfer ban was implemented on the Madrid club a deal was taken off the table.
The former Real Sociedad striker revealed he could not leave the club in such circumstances, claiming it would be "dirty".
However, rumours have not died down, but intensified as Barcelona are now said to have joined the fray.
After being left shocked by Neymar's decision to leave the club for Paris St-Germain, the Catalans frantically searched for a replacement in the dying embers of the transfer window.
They sought after Liverpool playmaker Philippe Coutinho, but had three bids rebuffed.
Eventually they settled for Dortmund winger Ousmane Dembele, who moved for a club-record fee of £135.5m.
As rumours continue to swirl, Atletico chief Cerezo has issued a response, stating that he is prepared to dig his heels in over any potential bid.
"Griezmann is an Atletico player and I tell you that I think he will be for a long time, and you know that I'm not lying to you," he told Spanish radio station Sport.
"Everything has its explanation, I've been around since the time of Fernando Torres saying if he's going or staying, they play where they want to play.
"Griezmann is a player of Atlético de Madrid. And you know I do not lie to you, players go up and down, but he's fine."
The 26-year-old stoked rumours that he would join the Red Devils after posting a picture to fellow linked star Mesut Ozil.