Manager Sam Allardyce pulled off one of the transfer coups of the summer when he persuaded the Cameroon international to join the Hammers from Barcelona on a season-long spell.
Song has lived up to his billing, producing some assured displays in the heart of the midfield and was a stand-out performer in Saturday's 2-1 Premier League win over Manchester City.
The 27-year-old is likely to have plenty of options at the end of the campaign if he maintains his form, but would rather stay in this country than return to Barcelona.
Song, who spent seven years at Arsenal before heading to Spain, told Sky Sports News HQ: "No, I think my future will be here.
"My family, everyone is happy here. I'm very happy to come back to England.
"I've always said if I move from Barcelona, I'll come to England and my future is here anyway. I just want to enjoy playing at the moment and we'll see what is happening at the end of the season."
The Hammers have moved up to fourth in the Premier League after last weekend's surprise victory over the reigning champions.
Defender James Collins hopes the side can extend their winning run to four games when they travel to Stoke.
"The confidence was obviously high beforehand, but obviously beating the champions at home - in front of our home fans - it breeds confidence throughout the whole club," said Collins.
"Not just with us, all the fans as well.
"Long may it continue and we look forward to Stoke on Saturday."