The 24-year-old, who joined the Hammers' youth academy as a 16-year-old before making his senior debut in 2007, has been linked with a Newcastle move.
But Wales international Collison, who has struggled with knee injuries to limit his appearances for the Londoners in recent seasons, has hinted he could spend his career as a one-club man.
He told the Daily Star: "I have been here for eight years and I don't want to go anywhere else.
"I have always wanted to be a West Ham player.
"It is like family to me and we're all local here. Everything I know is round here and I just don't see myself anywhere else."