Reports in England and Spain over the past week have suggested that Manchester United could make a move to sign the 28-year-old at the end of the Premier League season.
The Red Devils have seemingly been long-term admirers of the France forward, having been linked with a swoop to sign Griezmann on and off in 2016 and 2017.
However, Griezmann decided to remain at Atletico and put pen to paper on a long-term deal at the Spanish side.
Manchester United signed Romelu Lukaku in July 2017 to bolster their attack but the Belgium international has struggled to consistently hit top form at Old Trafford.
Griezmann, meanwhile, is thought to have grown disillusioned at Atletico Madrid, particularly after their 3-2 loss to Juventus in the Champions League round of 16.
But Morata, who moved to Atletico from Chelsea FC in January, is optimistic that Griezmann will remain committed to los Rojiblancos.
“It does not worry me. We have been very f***ed up by what happened last week, but I see Antoine happy here,” Morata is quoted as saying by Metro.
“I sincerely think so [Griezmann is happy at Atletico]. He is at home, he is our most important player, our flag player.
“The rest of the squad and the fans want him to stay with us. He is our reference player.”
Manchester United managed to book their place in the Champions League quarter-finals thanks to a 3-1 victory over Paris Saint-Germain in the second leg of their round of 16 clash earlier this month.
The Red Devils will take on Spanish giants FC Barcelona for a place in the last four, starting with a home clash against the La Liga side on Wednesday 10 April.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news