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Newspaper reports have suggested the 33-year-old, whose deal at the Britannia Stadium expires at the end of the season, could join former Stoke boss Tony Pulis at The Hawthorns.
But Hughes said: "There's nothing in it. People are adding two and two together and making five.
"He's a big part of what we're doing here. His future is with us."
Crouch was signed by Pulis in September 2011, joining Stoke from Tottenham for £11m.
The striker - capped 42 times by England - has scored 29 goals in 117 Premier League games for the Potters and has attracted interest from elsewhere, most notably when linked with QPR in 2013.
Crouch has started all but one of Stoke's last six games and provided the header from which Ryan Shawcross scored the opening goal in the 1-1 draw against Manchester United on Thursday.
"You saw by his performance he wasn't bothered by any speculation," added Hughes.
Rather than offloading a forward in January, Stoke could be stretched by Mame Biram Diouf leaving to play for Senegal in the Africa Cup of Nations and Bojan's hamstring injury.
The former Barcelona man missed the draw with United, but Hughes is hopeful of a swift return.
"We have had Bojan checked," said Hughes. "He has a slight tear, grade one. It can be 10 days out or a couple of weeks. Hopefully he'll be back soon.
"We asked the Senegal FA about Diouf. They are within their rights to call him up on what I think is 5 January.
"We hoped to have him for the game at Arsenal, but they said no."
Stoke City manager Mark Hughes has dismissed speculation linking striker Peter Crouch with a move to West Brom.