The Red Devils are expected to bolster their midfield ranks if Paul Pogba does leave this summer.
A recent report suggested that United were exploring a swap deal with Juventus involving Alex Telles and Adrien Rabiot, but the Premier League giants supposedly have their eye on one of Pjanic.
According to Fichajes.net, the Bosnian fits the bill in terms of what Man United are looking for.
The 31-year-old arrived at Camp Nou from Juventus last summer, but he has only started six top flight matches during a frustrating season under Ronald Koeman.
Pjanic has a deal at Camp Nou until 2024.