According to Calciomercato - as reported by PlanetaMilan - the Blaugrana have been impressed by Leao's performances at the San Siro and might make a move for him in the summer.
The report suggests that the Portuguese attacker is valued at €40m by the Rossoneri. But it is unknown if a cash-strapped Barcelona can raise that amount.
Messi is expected to depart Camp Nou this summer and the club have started turning to cheap alternatives to replace their iconic captain.
They have reportedly lined up an offer that will see them swap Francisco Trincao for his compatriot.
It remains to be seen whether AC Milan will accept the proposal, but the Serie A side are adamant that they will not consider any offer below their valuation.
Rafael Leao has been one of the driving forces behind AC Milan's title tilt this season. The 21-year-old joined the San Siro outfit from Lille in 2019 and has since made 54 appearances in all competitions for the club.
This term, he has weighed in with five goals and five assists from 17 Serie A games to help the Rossoneri to second spot on the table.
A swap deal for Rafael Leao does not make sense on any level for Barcelona
Barcelona's poor state of finances means that they might not be able to raise the requisite funds for Rafael Leao's purchase.
The veracity of their proposed swap with Trincao for Leao is unknown. But if true, it will represent yet another transfer gaffe from the Blaugrana board.
Francisco Trincao has begun to show his value to the club and is currently one of their most in-form players.
Although Leao has impressed, he has not done too much of note to suggest that his abilities are deserving of a club the size of Barcelona.
Both men are of a similar age, with almost equal windows of development. It therefore makes no sense for the Blaugrana board to sanction a swap either from a sporting or financial perspective.
At first glance, it might seem like an unlikely proposition. However, considering all the shocking transfer decisions made by Barcelona in recent years, it might not be far-fetched to suggest that a swap deal for Rafael Leao is in the works.