The France international was Manchester United’s first-choice target last summer and it looked as though a deal would be agreed once the transfer window opened.
However, Atletico Madrid had their transfer ban upheld which meant they would have been unable to bring in a replacement.
Griezmann subsequently committed to staying at Atletico for at least one more season, meaning United then turned their attention to signing Romelu Lukaku.
The France international’s release clause drops to £88m this summer though and the Red Devils have maintained an interest in signing the striker.
But reports in recent months have suggested Barcelona are now at the front of the queue to sign Griezmann.
And The Sun on Sunday claim the 27-year-old has agreed terms on a deal to move to the Nou Camp.
The report states Jose Mourinho had sustained hope that he would be able to tempt Griezmann into moving to the Premier League.
But Griezmann is now set to join up with Lionel Messi, Luis Suarez and Philippe Coutinho at Barcelona to potentially form one of the most lethal front lines in European football.
The La Liga leaders have already scored 76 goals this term with Messi and Suarez leading the goalscoring charts with 26 and 22 respectively.
Griezmann is fourth on the list, behind Cristiano Ronaldo, with 17 goals while also providing eight assists.
And his efforts in front of goal have helped put Atletico second on the league, although Barcelona sit 12 points ahead of them at the top of the table.