The former England skipper, who sat out the Toffees' final two games of the season with a knee injury, is a confirmed transfer target for Major League Soccer side DC United.
Amid suggestions that the move could go through in the next 48 hours, bringing an end to Rooney's association with his boyhood club, Allardyce was keen to play down repeated talk of a row between the two.
"I can update you on the fact that all the rumours, gossip, miscalculations and stories the media are writing between me and Wayne are absolute rubbish," he told Sky Sports News.
"They'll still continue to make it up that we've had a row, and that he's walked out on me, or that I've had a row with him and all that. I'll tell you now that me and Wayne have handled ourselves very maturely, very professionally, along this journey.
"Wherever the journey ends up at is not in my hands, it's in the board of directors' hands and Wayne's hands. I have just been the go-between and me and Wayne have dealt with that brilliantly up to now."