The midfielder on Thursday insisted he is happy to remain with the Shakers amid interest from rivals clubs, with Crawley - managed by former Shakers boss Richie Barker - rumoured to be one of those keen.
Chairman Fenton refused to name the club who have launched a bid for Worrall's services but admitted he thought it was "a joke" at first.
Fenton on Friday evening told Bury's official website: "I can confirm the club has today received a derisory offer for David Worrall.
"When it first arrived I actually thought it was a joke. David is a contracted Bury player with two years left on his contract, we want him here, and as he commented just a few days ago he is extremely happy to be at Gigg Lane.
"We object to clubs trying to unsettle our players and if David is ever to leave us in the future we would hope it is to a club that matches his undoubted talent."