Rooney missed Everton's final game of the season at West Ham United with a knee injury and has been widely reported by British media to have agreed a deal "in principle" to sign with DC United.
Allardyce has said that negotiations have taken place over Rooney's possible departure, but the 63-year-old former England manager is particularly unhappy with suggestions that the pair's relationship has broken down.
"All the rumours, gossip and miscalculating stories that the media are writing about what's happening between me and Wayne are absolute rubbish," Allardyce told the BBC after the 3-1 defeat.
"They will continue to make it up stories that we've had a row and he has walked out on me.
"Let me tell you, we've handled ourselves very maturely, very professionally. Whatever happens is out of my hands, it is in the hands of the board of directors and Wayne."
Allardyce's own position is under scrutiny, with some fans booing him on Saturday and calling for his dismissal during the defeat that meant Everton finished the season eighth on 49 points.
Allardyce said a meeting is planned with Everton majority owner Farhad Moshiri next week when some reports suggest he will be sacked.
"Whenever the board tell me what they want to do then I'll know. What will be will be. All I can say is that I came in to do what I wanted to do. The credit goes to the players."
Allardyce has a year remaining on his contract.
(Reporting by Neil Robinson; Editing by Toby Davis)
