The 28-year-old defender, who has made 28 appearances for the Tigers this season, is out of contract in the summer.
The former Fulham and Reading player told Sky Sports News: "I'm not in a position to beg for a contract. I'll let my football do the talking. I've got to do my best for the club, help them get promoted and, hopefully, I'll be a Premier League player next season.
"I'm not being arrogant, but for two years I couldn't see a better right-back in the league. I know I've got the right qualities.
"I'd like to stay and see the club do well and, besides, my nan would kill me if I did leave. That's another big reason to stay."
Hull are currently outside the automatic promotion places in the Championship table on goal difference.