The Blades are in the hunt for a new boss after sacking Nigel Clough and his entire backroom team on Monday.
But the Bantams are desperate to keep hold of Parkinson, who has a year left to run on his current contract at Valley Parade.
Bradford’s joint-chairman Mark Lawn said: “It’s true we’ve been contacted by Sheffield United.
“They want to speak to Phil, but we’ve turned their request down. We’ve made it perfectly clear that we want Phil to stay.”
When asked if the board will open talks with the 47-year-old over a new deal, Lawn added: “That’s up to Phil.
“We’d be happy to do that. He has another year left on his contract and he knows we always look to negotiate new contracts at the end of their terms.”
Lawn refused to comment on whether Parkinson had a get-out clause in his contract that the Blades had failed to activate.
“I’m not willing to discuss the finer points of Phil’s deal,” he added.
Parkinson penned a three-year deal at the end of the 2012/13 season after leading Bradford to the League Cup final and to promotion from League Two.
He guided the club to a seventh-placed finish in League One this season, missing out on the play-offs by four points.
Clough paid the price for the Blades’ failure to win promotion via the play-offs as they recently lost out to Swindon in the semi-finals.
The South Yorkshire club, searching for their eighth manager since being relegated from the Premier League in 2007, will embark on a fifth campaign in the third tier next term.