Everton are prepared to allow Bernard to leave this month.
The 28-year-old has been on the fringes of Carlo Ancelotti's side with nine appearances in all competitions.
Bernard's agent, Adriano Spadotto, admitted a loan move to Roma could be complete this month.
The winger joined Everton on a free transfer from Shakhtar Donetsk in 2018 and has seven goals and seven assists in 75 appearances.