The striker has risen to prominence over the past few weeks thanks to a string of fine performances for Ghana.
Reports have suggested that he could now leave Rennes before the end of the summer, with a switch to England his preferred option.
Gyan concedes that he is flattered to be linked with West Ham, while he has also heard good reviews about Sunderland from Ghana team-mate John Mensah.
However, he insists he does not have a problem with Rennes and is prepared to let them have the final decision.
"I always dream about playing in the Premier League. The sooner the better," the 24-year-old said. "I want to test myself against all the biggest and best defenders in the English league.
"Sunderland? Mensah said they are a good team.
"West Ham is attractive because they are in London and that is a great city that I love.
"But Rennes will have their say, I still have a contract with them and they are great people there. So let's wait and see."
Gyan's World Cup ended in heartbreak as Ghana bowed out to Uruguay on penalties at the quarter-final stage.
Gyan scored in the shoot-out but missed a spot-kick in the closing seconds of extra-time that would have sent Ghana through to the last four.
He has now come to terms with the disappointment, saying: "I am very well. I sometimes think about the penalty miss but that is normal, there was a chance to make history.
"But it is God's plan and I am a great believer so it is fine for me."