But it is understood they also face competition from Italian giants Juventus for the central defender.
According to Italian outlet Calciomercato, Chelsea have made attempts to sign the Italian star in the past.
And with Maurizio Sarri's side facing a two-window transfer ban, potentially postponed until next year, they may try their luck this summer.
But while the Blues continue to monitor his situation, rivals Manchester United are also thought to be keen on Romagnoli, 24, who is comfortable playing out from the back and has been compared with Alessandro Nesta.
It is no secret the Red Devils want to bring a new centre-back in at Old Trafford.
Napoli star Kalidou Koulibaly has been a long-term target from Serie A but could cost the club as much as £90million.
Former Roma defender Romagnoli – who signed a new deal at AC last summer keeping him at the club until 2022 – is unlikely to cost that much but could be tempted by a move to Juventus.
The Old Lady have won the last seven Serie A titles and are on course for eight in a row.
When Leonardo Bonucci returned to Juventus after his one season with AC Milan last term, manager Gennaro Gattuso needed to appoint a new club captain.
Controversially, he opted for Romagnoli with Ignazio Abate as vice-captain.
But Gattuso feels his decision has been justified and now expects his captain to play an important role in the club's future.
He said: "It is priceless, it is scarce and it is right that he is with us. I was also massacred for making him captain.
"He is now empowered, has great room for improvement. It can be a player who can write important pages with this shirt. In the last year and a half he has found the key inside his head, he is taking better care, he does things with criteria."
AC Milan legend and former captain Paulo Maldini backed the call, adding: "He is a silent player, at the age of 23 I was not ready to have the captain armband.
"At that age I was struggling to transmit certain things. A very rapid growth is needed from this team and he has grown a lot from this point of view."
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