The 26-year-old moved north in January but had to wait until the home defeat to Manchester United earlier in April to make his first start for the Wearsiders.
He has since started against Hull City and wants to extend his stay with the Black Cats as he feels settled and happy.
Davenport has not settled at a club since his transfer from Coventry to Tottenham in 2004, being loaned out on three occasions during his time at White Hart Lane.
He then signed for the Hammers in January of 2007 but has since been sent on loan on two further occasions.
Davenport told the Sunderland Echo: "Since I've been up here I've loved every minute of it.
Unbelievable"Everybody from the manager to the tea ladies have been unbelievable. So if I can stay I'll be delighted. But the main thing is getting results first and foremost and seeing what happens in the summer.
"I've had a lot of injury problems and being at Tottenham, it was a massive club. It forced me to go out on loan to play week in, week out.
"If I can find somewhere where I'm settled and happy, as I feel I am here, I'll be happy. Who knows?
"I've settled in well. I've got a young family and my daughter's at school down south so they're up at the weekends. We're in Durham and the family really like it. Credit to the club, everything has been fantastic."
Sunderland take on West Brom at the Hawthorns on Saturday and victory will go a long way to securing their survival, although Davenport is taking nothing for granted.
TrustHe said: "I was saying to the lads, they're a team who trust each other with the ball, pass and move, pull you into areas and pop it around you.
"We're going to have to be nice and compact down there. Whereas the game at the weekend was played at a high tempo, we'll have to give them a bit of respect in terms of their quality on the ball, even though they're bottom of the league.
"We might have to nick it off them and hit them quick. With Djibril Cisse and Kenwyne Jones' pace maybe we can hit them that way.
"There's absolutely no pressure on them and it comes from the manager. If you listen to him he wants them to go out, express themselves and play a certain way.
"It's quite easy to fall back on the fact it's a results business, but he's got a belief in the way they play and they stick to it.
"It's up to us to make sure we prepare right and get the result we want."