Butland has been named as one of Chelsea’s potential targets if Thibaut Courtois leaves.
Courtois has been strongly linked with a move to Real Madrid and a return to the Premier League with a top six club would appeal to Butland, but Rowett is not convinced by the speculation.
Rowett said: “I don’t believe any rumours if I’m honest. I understand the good players are going to be linked with good clubs which is great, I get that.
“That shows the level of player we’ve got at this club.
“It shows the level Jack Butland is at as a young keeper and that those clubs might potentially look at him.”
According to Sky Sports reporter Rob Dorsett, Butland and Kasper Schmeichel are the two players on Chelsea’s wishlist to replace Courtois.
And speaking on the Sky Sports Transfer Talk podcast, Dorsett claimed a transfer merry-go-round could occur.
He said: “We’ve learnt this week that he’s on Chelsea’s list of potential replacements if Courtois leaves.
“And we fully expect Courtois to leave don’t we as he goes into the last year of his contract.
“We think he’ll go to Madrid and so because of that you’ve got Butland and Kasper Schmeichel who is on Chelsea’s list as well we’re told.
“So there’s a couple of possibilities here. Either Butland goes to Chelsea straight away, job solved or Schmeichel goes to Chelsea and I think Leicester would be very interested in Jack Butland.
“So there’s a bit of a merry-go-round, a bit of a domino effect going on there again.”