Griezmann is being strongly linked with a move away from Atletico Madrid after his manager Diego Simeone admitted last week they would find it tough to keep him if a big club made an approach.
The France striker struggled for goals earlier in the season but interest in the 26-year-old has not diminished.
Manchester United and Barcelona are among the clubs keen on signing Griezmann and keeping tabs on the forward.
Rumours in Spain claimed Bartomeu had met with Griezmann’s family to discuss the transfer.
However Amor was reluctant to confirm whether discussions had taken place but said there was already a good relationship with Griezmann’s entourage.
“If Bartomeu met with Griezmann’s family as the newspapers say, then there may well have been an approach,” Amor told Movistar.
“Though, I don’t know anything for sure.”
He added: “There is a good relationship, there can also be comfortable conversations.
“Rumours are inevitable in the football world. In Griezmann’s case there are many people we talk to; it’s our obligation to have contact with players.”
When asked if Barcelona would make a move for Griezmann, manager Ernesto Valverde was also coy.
“Griezmann is a great player who is on another team, he is not in ours,” Valverde said.
“I like our team very much.”