The goalkeeper has made 11 appearances for the Toffees this season, and is said to be putting good pressure on Everton number one Jordan Pickford to ensure competition for the place between the posts.
Olsen has not featured for his parent club Roma since 2019, as the Italian club sent him out on loan last season as well, where he made 19 appearances for Cagliari.
Ancelotti has said that he wants the Swedish keeper to become a permanent member of his squad, telling reporters: "Robin Olsen was back for the past two games after a difficult time.
"He is a fantastic guy and a really good goalkeeper. We like having him at Everton and hope this can continue."
Everton currently sit eighth in the Premier League, six points behind West Ham United in the Champions League places.