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The Owls claim that they have had a £200,000 bid turned down by Luton for the 27-year-old, who still has a year left on his contract.
But Hatters' boss Mike Newell slammed Wednesday for trying to unsettle Howard, and confirmed that no bid has been received.
Newell told BBC Three Counties Radio that he doesn't want to sell his best players, and that as far as he's concerned there has been no bid.
He also accused Wednesday, who finished in the bottom half of the league, of going behind his back to try and sign the player.
Howard bagged a brace against the Owls in Luton's 3-2 win in the final game of the season at Kenilworth Road.
He was first approached by Wednesday at the start of last season.