Ayew was Swansea's top scorer during last season's successful survival bid, netting 12 goals in 34 Premier League games.
Andre Ayew celebrates after scoring the first goal for Swansea
Reports have suggested that the Swans could be willing to listen to offers of around £15 million for their top scorer, who fired home 12 goals as part of his team's successful survival bid last season.
Swansea manager Francesco Guidolin
Ayew is understood to be happy to stay in South Wales, although he may still be tempted should Chelsea come back in with a new bid, with the Blues previously seeing a £10 million offer knocked back in January.
Speaking about his future on French television last week, Ayew admitted there was interest in his signature, before hinting that the chance to play in the Champions League - something that Chelsea currently cannot offer - could prove too good to turn down.
"I like England. I feel good at Swansea. It was a good year for me. The season was good on a personal level," he said.
"Of course, every player wants to play for the Champions League or the title. A time will come when I'll aim for these."
Sunderland are also thought to have an interest in the 26-year-old, but Guidolin still hopes to keep his star player at the Liberty Stadium.
Andre Ayew celebrates scoring the second goal for Swansea
However, the Italian wants the Ghanaian to stay in his current role as a striker, despite the player insisting it is not his preferred position.
He told Wales Online: “He says he is not a striker and that he is a midfielder, but he has done well and in my opinion he is a striker and a good false nine. They are good characteristics we have discovered with him and I hope he stays.
“He is a big player, but his attitude is good. He is an important player, but he is quiet, a good guy, he decides to stay here and he is happy.”
Swansea manager Francesco Guidolin before the game