The Italy international will be allowed to leave Florence for the right price this summer by club owner Rocco Commisso.
La Nazione says Chiesa's future remains unclear with Fiorentina and suggest United have lodged a €55m offer for the Italian.
Just this week, Commisso stated: "I kept him last summer, now I hope that he remains, but if he wants to leave, then he can do so as long as he brings in the right money for his true value.
“I gave him the all-clear, as long as he brings the right money.
"I would like him to stay, but if he does want to go, then the clubs have to pay us what we believe he is worth."