The midfielder is reportedly a top summer target for the Blues as they look to bolster their squad after a disappointing season.
And, according to Corriere dello Sport, Chelsea have stepped up their interest in the France international.
Scouts were said to be in Milan on Wednesday to watch Pogba as Juventus took on Inter in the second leg of their Coppa Italia semi-final.
Juve went into the clash 3-0 up on aggregate, but lost the match by the same scoreline to send the tie into extra-time.
The Italian champions did, however, hold their nerve to win on penalties – with £70m-rated Pogba scoring his spot-kick.