The chance to sign a young, €60m-rated goalkeeper on a free transfer would appeal to many clubs.
Romano reports that Chelsea made an approach for the 21-year-old Italy stopper in recent months.
However, the English side did not follow up with any sort of official offer.
Chelsea eventually signed Edouard Mendy which presumably put an end to their interest in Donnarumma.
The feeling of many interested clubs is that Gigio really wants to stay at the San Siro, a view Milan bosses also take.
However, the Rossoneri are still yet to find an agreement with Donnarumma and his agent Mino Raiola.
Donnarumma wants a salary in excess of €6.5m-per-season to commit to a new long-term deal.
Time is now ticking, but Milan are hopeful of renewing Donnarumma’s contract in the coming months.
The Milan youth product has already made 209 first-team appearances at the age of 21.
Donnarumma is also firmly established as Italy’s number one, having won 20 caps since 2016.