Roma remain locked in talks with United over a permanent deal for Smalling, who has impressed on loan at the Italian giants during the 2019-20 campaign.
However, it is thought that the two sides are struggling to agree a fee for a player who still has two years left to run on his contract with Ole Gunnar Solskjaer's side.
According to Calciomercato, Juve are now weighing up an approach for the 30-year-old and could offer Bernardeschi to the 20-time English champions in exchange.
The Italy international has been a regular for the Old Lady during the 2019-20 campaign, contributing two goals and two assists in 37 appearances in all competitions.
Bernardeschi has less than two years left to run on his deal with Maurizio Sarri's side.