Chelsea are willing to offload Loftus-Cheek but his £150,000-a-week wages represent a stumbling block for clubs interested in signing the 27-year-old.
Champions League semi-finalists Milan hope to convince Loftus-Cheek to join fellow Chelsea academy graduate Fikayo Tomori at San Siro.
But he remains reluctant to leave his boyhood club and, despite having only one year left on his contract, would need to be forced out by the incoming manager at Stamford Bridge.
Several homegrown Chelsea players face uncertain futures and Loftus-Cheek is a player the owners at Stamford Bridge would like to leave.
Loftus-Cheek rejected a move away in January when he was made available for transfer in the last two days of the transfer window.
He was put up for sale with little notice alongside Gallagher, who refused a £45million move to Everton after being blocked from talking to Newcastle due to their status as rivals for Europe.
The sale of academy graduates will help Chelsea ensure they continue to stay in line with Financial Fair Play rules.
Selling some homegrown stars would be pure profit under the new version of UEFA’s financial sustainability rules, and selling Loftus-Cheek, Mount, Gallagher, Levi Colwill, Callum Hudson-Odoi and Trevoh Chalobah could generate around £200m.
Chelsea have identified a striker, a midfielder and a goalkeeper as their transfer priorities this summer but those plans could change once Pochettino is appointed.
Napoli striker Victor Osimhen is admired but he unlikely to join team not in Europe, while Inter’s Andre Onana, Dortmund’s Gregor Kobel and Brentford’s David Raya feature on the goalkeeping shortlist.
Chelsea have a £28m option to buy to make Denis Zakaria's loan move permanent but are not likely to take it up.
They will also take a look at 19-year-old midfielder Andrey Santos, who is currently on loan at Vasco da Gama, during pre-season.