Welbeck, 20, has made a good impression since moving to the Stadium of Light on loan from Manchester United in August and is an important part of the England Under-21 side.
However, although he was born in Manchester, Welbeck's parents are Ghanaian and Gyan believes there is a chance he will opt to play for the Black Stars.
"I have spoken to him, and I think he might play for Ghana, but I am not really sure of that for now," Gyan told KickOffNigeria.
"He's young and he has not made up his mind yet. He says we should give him enough time to think about it, but we all hope he comes as he is such a fantastic young player."
"Before I came to Sunderland, I spoke to Mensah and he told me a lot of good things," Gyan said. "We are like a family now and playing at Sunderland is like playing in the Ghanaian national team."