"AC Milan categorically denies what was published today in the pages of the Corriere della Sera regarding its manager Massimiliano Allegri," the club said on their website on Saturday.
Milan-based daily Corriere della Sera said Allegri had accepted a three-year contract to move to the Italian capital after refusing a deal with Inter Milan.
"AS Roma categorically denies today's report in Corriere della Sera... which refers to an alleged agreement made with Mr Massimiliano Allegri," Roma said.
Inter have also denied that there has been any contact between them and Allegri regarding him taking over from under-fire Andrea Stramaccioni.
"Regarding what was reported in today's edition of the Corriere della Sera on the future of the Nerazzurri bench, Internazionale categorically denies that has been any contact or requests for contact with AC Milan manager Massimiliano Allegri," Inter said in a statement.
Allegri's position with Milan has never been secure despite a strong second half of the season during which they have only lost one game, to leaders Juventus, and have climbed to third in Serie A.
They are a point ahead of Fiorentina and play three of their last four games against relegation strugglers Torino, Pescara and Siena, making them favourites to take the third Champions league spot.