The 21-year-old has reportedly attracted interest from Ligue 1 rivals St Etienne as well as a number of other clubs from Europe.
However, Ayew has insisted that he wants to stay and fight for his place at Marseille.
"I believe I have learnt to be patient. I don't want to leave. I have everything at this club to be a success," Ayew told L'Equipe.
"You always want more, but I won't complain. I played a lot of matches last season. My work will pay off – I don't know when, but it will pay off."
Ayew's current deal at Marseille expires in 2015.