The 23-year-old goalkeeper is out of contract in the summer and is reportedly chasing a €10million a year deal, running for two years. However, Milan are offering €7.5million and want to tie Donnarumma to a five-year contract.
United and Chelsea are both waiting in the wings and are reported to have already had discussions with Donnarumma's agent Mino Raiola.
Donnarumma will be afforded the perfect audition for a move to Old Trafford on Thursday when United host Milan in a Europa League round-of-16 first-leg tie.
United are 2/5 to progress, with Milan at 7/4.
Pep talk with Sergio Aguero won't come until season-end
"We have to be calm," said Guardiola. "The club will speak to his agent to discuss the situation and we are going to talk at the end of the season."
However, Guardiola's lack of urgency on the matter could open the door for a move with Aguerro entertaining a number of offers from clubs in Europe and mulling over a return to South America to end his career in his homeland.
A return to Argentina and any Argentine Primera club is 4/1.
Centre for arbitration after England vote to introduce equal pay
RUGBY UNION: England captain Owen Farrell will be paid the same during the Guinness Six Nations as uncapped Wasps centre Paolo Odogwu after senior players voted to restructure a pay deal report The Times.
All squad members will now receive an equal share of a £2.1million pot, with every player in camp for the duration of the championship receiving around £75,000.
Now blessed with a spirit of solidarity, England, who have lost two of their first three fixtures, are 5/6 with Bet365 to return to winning ways against France next time out.
* All odds correct at time of publication