Griezmann's buy-out clause has fallen from €200m to €120m, but Bartomeu said his club are trying to reach a deal without paying the clause.
Barcelona's attempt to sign Antoine Griezmann hit a setback after Atletico Madrid accused the Catalan club of negotiating with the player without its consent before his contract was over.
Given the occurrence of events over the past few weeks, PSG, well aware of the fact that Neymar has to depart, seem to have offered Real Madrid the chance to sign the Brazilian forward just so that he doesn't leave the club to go back to Barcelona.
World Cup victor Griezmann has a release clause of €120 million in his contract.
Atletico Madrid have launched a stinging attack on Barcelona and their own player Antoine Griezmann by claiming they secretly negotiated a transfer in February.
It added: "Atletico Madrid wants to express is strongest condemnation of the behaviour of both parties, in particular Barcelona, for having induced the player to break his contractual relationship with us during the moment in which the club was not only playing the Champions League tie with Juventus, but also challenging Barcelona for the La Liga title". "We know Neymar wants to leave PSG but we know that PSG do not want Neymar to leave". During the last season, he scored 28 goals, made 13 goal assists in 28 appearances.
Brazil global Neymar left Barcelona for PSG in 2017 for a world record fee of 222m euros (£200m) and has been linked with a return.
Speaking at a press conference after unveiling new signing Frenkie De Jong, Bartomeu offered an update on Barcelona's efforts to sign Neymar.
Griezmann would not be guaranteed to walk into Barca's starting line-up, though, with Lionel Messi, Luis Suarez and either Philippe Coutinho or Ousmane Dembele usually making up their front three last term.
The Barca president also provided an update on Griezmann, who already confirmed a couple months ago that he will leave Atletico.
Barcelona have already signed De Ligt's global team-mate Frenkie de Jong from the Dutch champions.