Sky Sports believe that Judge is unhappy at Griffin Park, after Brentford rejected a bid for the wide man from the Owls earlier in the month.
But Holloway does not think that the 27-year-old should put pressure on his current club to sell him.
"When you have a good season and start scoring goals, you get people in your ear about how well you're doing and which clubs want you,” Holloway explained.
“Unfortunately, the game is run differently these days and agents are far too involved.
"The facts are you've signed a contract, Brentford don't want to lose you so you've got to get on with it. The agent, who wants his player to move for his own interest, is the one putting these noises out and it's all a bit of a mess.
"Judge has knuckled down and kept on impressing people with his performances. Fair play to him. He's got to do what's best for him and his family. He's a really talented boy and he should just keep doing what he's doing.”
Wednesday are believed to have made Judge one of their top targets, and they remain interested in him.
Brentford, however, are demanding a £8 million fee for the 27-year-old, according to Sky, and that price could put Carlos Carvalhal’s men off.
If Judge does kick up a fuss at Brentford, he will be the second player in their current squad to have tried to force through a move this window - after James Tarkowski refused to play for Dean Smith’s side against Burnley.
Brentford have also lost Toumani Diagouraga to Leeds United earlier today and they will not want to see more players leave without sufficient replacements coming in.