The Spanish capital club made it to the two Champions League finals in last three seasons, losing both of them to local rivals Real Madrid. The 25-year-old has been heavily linked with a move to United and the Red Devils manager Jose Mourinho has made signing the France international as a priority in the summer transfer window.
According to The Sun, United have already discussed personal terms with the Atletico star under which Griezmann will be offered weekly wages of £220,000 ($276,584). Gerrard, who returned to Liverpool as a full-time academy coach, believes the La Liga attacker will consider making a switch to Old Trafford after the end of the season.
"He's playing in the Champions League for Atletico Madrid. He's got a chance of competing for that, which they have done for the past couple of years," Gerrard told BT Sport, as quoted by the Mirror.
"And he's probably thinking: 'Yeah, Manchester United probably is a good move, but it's still going to be there in the summer."
Atletico manager Diego Simeone has admitted that he will not prevent Griezmann from joining United if he is determined to leave his current employers. The Telegraph claims the player is valued to be around £86m ($108.1m) and United will make an approach to sign him.
"I don't tie anybody down. I simply work in order to continue getting better for the good of the club," Simeone said, as reported by the Telegraph.
"He [Griezmann] is in an extraordinary moment. He is working well, he has got back on the score sheet. He is currently in great form and it's normal that the top clubs in the world want him. I'm not surprised that those that can afford him are seeking him."