Krovinovic, 24, spent last season on loan at The Hawthorns, making 40 appearances in the Championship.
Slaven Bilic wants to hold on to Krovinovic after he played an important part in West Brom’s return to the Premier League.
According to A BOLA, one of two things could happen: an immediate sale or a loan with an obligation to buy.
Benfica will accept a fee of around €10m (£9m) for Krovinovic, whether it arrives now or next summer.
Until a deal is agreed, Krovinovic will train alongside other loan players who are waiting to learn their futures.
Krovinovic joined Benfica from Rio Ave in 2017 and was part of their 2018-19 title-winning squad.
However, a shortage of game time led to the Croat moving to West Brom last season, where he impressed.