According to the Spanish outlet, Bartomeu met to discuss the deal which is estimated to cost £87million (100m euros). "Though, I don't know anything for sure".
"There is a good relationship, there can also be comfortable conversations", he admitted.
It is inevitable in the world of football.
He eventually turned down the chance to move to Old Trafford, but United continue to be linked with the player, who reached the final of the Champions League and European Championships in 2016.
The Spain global defender told Onda Cero on the Griezmann rumours: "We are talking about a top player that has been doing really very at Atletico in recent years, any reinforcement would be welcome".
Reggie Bush: 'I'm done' after 11 NFL seasons
He finished his career with 1,286 carries for 5,490 yards and 477 receptions for 3,598 yards. He was also part of the Saints team that won Super Bowl XLIV.
However, he remained at Atletico as the club were unable to source a replacement due to their transfer ban.
"In the case of Griezmann, there are many players with whom one can be talking and engaging in some kind of relationship in case there is an opportunity".
The upheaval during the summer seems to have been detrimental to the forward's form this season though with Griezmann failing to hit the heights he set last term.
Barca are unlikely to be the only club keen to sign him in the next few months, but they could well have got a jump on any potential rival suitors if Bartomeu has met with Griezmann's family already.