The club are likely to lose a raft of players if their relegation fears are confirmed but goalkeeper Foster, who has been at the club since 2011, has no intention of jumping ship.
"I'll be here," the 35-year-old told British media.
"I've got no interest in trying to move clubs. I'm very settled and I'm sure there are quite a few others who would love to stay and help us get back to the Premier League.
"If we end up in the Championship next season we've got to bounce back up. I'd like to keep a core of the players that want to dig in, work hard and be in a tough fight to get out of the Championship, because it is a tough fight."
First-team coach Darren Moore took charge at the Hawthorns against Swansea and Foster believes there had been an immediate improvement in the atmosphere at the club following manager Alan Pardew's departure last week.
"Mooro took the bull by the horns last week and really raised the spirits around the place and the players and fans really bought into that," Foster added.
"Everybody would like to finish strongly, not only for themselves, the club and the fans, but for Mooro. He really does deserve it."
West Brom next visit second-placed Manchester United on Sunday.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
