Mancini was seen at Milan headquarters on Monday, where he held a 30-minute meeting with Rossoneri vice-president Adriano Galliani. The Manchester City boss played down the talks, describing it as nothing more than a courtesy visit and adding: "Milan fans can stay calm." Nonetheless, speculation has been rife over the content of the discussions.
City have long been linked with a move for Ibrahimovic, who worked under Mancini at Inter Milan, but Gazzetta dello Sport, Tuttosport and Corriere dello Sport were all reporting on Tuesday morning that the meeting was to discuss a potential deal to sign defender Thiago Silva. Potential swap deals involving Mario Balotelli and Carlos Tevez have also been suggested.
However, Allegri insists Milan will not allow their key players to depart, with the club looking to build after a disappointing season in which they won only the Supercoppa Italiana.
"The club and the president are keen to maintain AC Milan at a high level," Allegri told the AC Milan television station. "Ibrahimovic and Thiago will remain here.
"Thiago is young and Ibrahimovic can also give a lot. They are two champions on which Milan can build its basis for the future. The club is only working on replacing those players that have left."