The 24-year-old has already agreed personal terms on a four-year deal with the Italian giants.
talkSPORT revealed in April how the USA international was in line to leave Stamford Bridge having been deemed as surplus to requirements.
And this has led Milan to look to bring the forward to the San Siro ahead of rivals Juventus and Napoli.
French side Lyon have also been keen to snap up Pulisic, with the Ligue 1 outfit making an offer to sign the player last weekend.
But he rejected the approach, with his main priority this summer to secure a move to join the Rossoneri.
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Should Pulisic link up with Milan, he would be reunited with ex-Chelsea teammates Olivier Giroud, Fikayo Tomori and Ruben Loftus-Cheek.
Loftus-Cheek only made the move to Stefano Pioli's side earlier in the week in a £15million transfer.
Chelsea have been been open to selling Pulisic this window with the ex-Borussia Dortmund star having a year left on his contract.
Since arriving from the Bundesliga outfit in a £58m deal in 2019, Pulisic has struggled for consistency at Stamford Bridge.
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His first campaign showed huge signs of promise after he banged in 11 goals in 34 games - including breaking the deadlock in the 2020 FA Cup final defeat to Arsenal.
He was rewarded with the No.10 shirt following Willian's departure, with his next season seeing him win the Champions League, where he came on as a second half substitute in the 1-0 win against Manchester City.
Pulisic soon began to lose his place in the line-up, with last term seeing the player feature in just 24 Premier League matches.
He started just eight times in the top-flight, which saw Chelsea finish the campaign in 12th spot - the first time they had finished in the bottom half since 1996.
And Pulisic unsurprisingly failed to make an impression from his limited game time - chipping in with just one goal and as many assists.
Commenting on his future last month, he admitted he wanted to leave Chelsea in order to 'find joy again'.
He told ESPN: "It's absolutely a time where I need to figure out what's going to be best for my future and be somewhere where I can go and play and be trusted and feel good in what I'm doing.
"I want to find that joy at club level again, for sure."