The 31-year-old has played 11 times in all competitions for the club this term, and has rotated effectively with England star Jordan Pickford.
Olsen is due to head back to Roma when the season concludes, but Ancelotti hopes the club can make him a permanent member of the squad before next season begins.
"Robin Olsen was back for the past two games after a difficult time [family issues]," Ancelotti said, per the Liverpool Echo.
"He is a fantastic guy and a really good goalkeeper.
"We like having him at Everton and hope this can continue."