Mundo Deportivo says Barca had identified Rashford as a replacement for Neymar in 2018 and made contact with his camp at the time.
The feedback was encouraging, with Rashford's deal then expiring in 2020.
Indeed, it's claimed his brothers had committed to a deal and it appeared Rashford would be on his way, only for the striker to get cold feet at the last moment.
Rashford, at 21, was worried about how he would adapt to a new country and new language, along with where he would fit inside Barca's star-studded locker room.
It's also suggested Barca's interest forced United to upgrade Rashford's deal, which he signed on July 1, 2019, through to 2023.