The France international was heavily linked with a move to Old Trafford in the summer. However, after the Court of Arbitration for Sport (CAS) upheld the La Liga outfit's transfer embargo the 26-year-old remained with Atletico.
Griezmann signed a new deal at Wanda Metropolitano and his release clause will be set back to €100m (€100m (£87.9m, $118m) from 1 July. Jose Mourinho's side are still believed to be interested in signing the attacker, while Barcelona have also joined the race for his signature.
Mundo Deportivo reported in November that the Catalan club have an agreement in principle with the former Real Sociedad forward with a view to joining Barcelona next summer. The Independent claims senior figures at Atletico and United believe the Frenchman will end up at the Nou Camp, despite interest from the Red Devils.
Simeone has now opened the door for Griezmann to leave Atletico and believes he can flourish if he decides to join an attacking team.
"I always say the same thing. I love my players a lot. I love that they grow up. I am not ungrateful," Simeone told L'Equipe.
"If a player comes to me and says: 'Coach, I have a chance of a lifetime to play for a certain team, I want to leave'. If he gave his all for me as Griezmann does, I'll say it's no problem. I know that he needs to grow.
"Of course Griezmann will be able to leave at some point, just as Diego Costa and Arda Turan were. If one day Griezmann leaves Atlético and goes into a more offensive team, he will be much better. Of course, because he needs an attacking game."
The Argentine coach also issued a warning to potential suitors that Griezmann will not be at his best if he is forced to play alone up front.
"He is one of the players who has grown the most since I came to Atletico. But he needs an attacker in front of him. He is not a reference in front of goal like Neymar, Ronaldo or Messi can be. He needs another player to create opportunities," he explained.
"We managed to make Griezmann better, there is no doubt about it. How long has he been here? Three and a half years? The numbers speak for themselves.
"[A striker at Atletico] doesn't play like one at Paris Saint-Germain, Barcelona or Real Madrid, because in eight games the PSG or Barca striker will score seven. Atletico's will score five or six. So, we need to make the effort.
"Attackers who score seven in eight can afford to do less defensive work because they are sharper in front of goal. At Atletico - or in the teams I consider weaker than Real, PSG, Bayern and Barca - the attackers must put in extra work to compete.
"To put it another way, Neymar, Messi, Robert Lewandowski and Ronaldo are decisive. Their defensive work will be less important as they are sharp in the penalty area. All others are less efficient, so they need to work more."