Olsen played his second game for Everton on 16 December 2020, away from home in the league against Leicester City. Everton won the game 0–2 with Olsen keeping a clean sheet. Olsen also kept a clean sheet in his last game for Everton against Brighton & Hove Albion 12 April 2021. The goalkeeper impressed on the occasions he stepped into the side in place of Jordan Pickford. Despite Carlo Ancelotti's initial desire to bring the 31-year-old to Goodison Park on a permanent basis, the surprise exit of the Italian in the summer seemingly scuppered any hope of that taking place. While Everton instead brought both Asmir Begovic and Andy Lonergan to Merseyside to provide back-up to Pickford, Olsen opted to move to Sheffield United on loan.
