The Mail on Sunday says Anuradha Desai, the Indian businesswoman who heads the Venkys conglomerate which owns Rovers, has written to the Premier League to express concern that United may have spoken to Jones's agent about a move to Old Trafford before Rovers had given them permission to do so.
Blackburn's letter, which was received by the Premier League on Friday, is not a formal request for an investigation or an official complaint over United's conduct.
Desai said: "We have reasons to believe that the player's agent and maybe the player had been in touch [with United] for two to three months before permission was granted.
"I was ready to take Manchester United on, ready to go to a tribunal if that's what it led to. But we spoke at length to [Blackburn manager] Steve Kean and we knew Phil wanted to go to United.
"We concluded that the person who would be most damaged by a delay and legal action was Phil. That wasn't fair on him. There was a release clause for £16.5m and the total deal was £4m more with the add-ons. We wish Phil well."