The Reds are understood to be open to the possibility of allowing their target man to spend a year in Italy, with agreeing a financial package thought to be the main issue
Milan owner Silvio Berlusconi's Sport Mediaset are reporting the two clubs are negotiating a season-long loan with a view to a permanent deal worth around £13.5 million [€17m].
The Merseyside club are thought to be open to letting Carroll spend the season in Italy, but are looking for an initial payment of around £2.4m [€3m], while Milan are offering around £1.2m [€1.5m].
Carroll's future has been the subject of much speculation since new boss Brendan Rodgers arrived at Anfield in the summer, while Milan are in the market for a striker to fill the void left by Zlatan Ibrahimovic.
In recent months both West Ham and Newcastle have also expressed an interest in Carroll, who has failed to find his best form since arriving at Anfield for £35m in January last year.