The France international was again in strong form for Atletico during the 2023-24 campaign, scoring 24 goals and registering eight assists in 48 appearances in all competitions.
The 33-year-old has another two years left to run on his deal at Wanda Metropolitano, but according to L'Equipe, there is a clause in his contract allowing him to leave for £12.8m in the upcoming market.
Teams from the MLS are said to have registered their interest, with Griezmann previously revealing that he wants to finish his career in North America.
There is also thought to be significant interest from Europe, but the forward said at the end of last year that Atletico would almost certainly be his final club in European football.
Griezmann is currently preparing to represent France at this summer's European Championship.
Elsewhere, Crystal Palace are reportedly exploring the possibility of moving for Leeds United attacker Crysencio Summerville during this summer's transfer window.
The Eagles are bracing themselves for offers for Michael Olise and Eberechi Eze, with a number of major clubs believed to be keen on the duo.
According to The Mirror, should either Olise or Eze depart in the upcoming market, then Palace are likely to move for Summerville.
The report claims that the London club are long-term admirers of the 22-year-old, who is thought to be valued by his Championship outfit in the region of £30m.
Chelsea, Aston Villa and Liverpool have also been credited with an interest in the Dutchman, who has two years left to run on his contract at Elland Road.
Summerville scored 21 goals and registered 10 assists in 49 appearances for Leeds during the 2023-24 campaign, including 19 goals and nine assists in 43 Championship fixtures.
Meanwhile, according to Football Insider, Nottingham Forest have signalled that they are willing to accept £4m for Joe Worrall this summer amid interest from Sheffield United.
The 27-year-old is not believed to be a part of Forest's plans moving forward.
A number of Championship clubs are said to be keen on the centre-back, with Sheffield United seemingly at the head of the queue following their relegation from the Premier League.
Forest will allegedly accept £4m for the defender, who spent the second half of the 2023-24 campaign with Besiktas, making nine appearances for the Turkish club.
Worrall has made 226 appearances for his current team in all competitions, including nine outings last term, but he was allowed to leave on loan at the start of February after losing his starting role at the City Ground.