Coutinho has impressed on his return to the Premier League, with Gerrard previously stating he wants to retain the Brazilian winger on a permanent deal.
The current agreement with La Blaugrana expires at the end of the 2021/22 season, with Barcelona still paying the majority of his wages.
However, the two parties agreed to a €40m purchase clause in the initial deal, with Coutinho’s Camp Nou contract up at the end of 2022/23.
Gerrard admitted Villa may push to lower that fee, if they agree to release Barcelona from a salary contribution, in the next 12 months.
“Obviously, we want Coutinho here next season,” as per reports from Marca.
Coutinho has already managed four goals and three assists in domestic action despite Villa failing to challenge for a European qualification spot.