The Toffees announced the signing of centre-back Ben Godfrey from Norwich City earlier today and have turned their attention to landing a goalkeeper.
Carlo Ancelotti is keen to add a new custodian to his ranks to challenge England international Jordan Pickford, who has been prone to errors in goal.
Everton have looked at a number of goalkeepers in the final hours of the transfer window and, according to Italian broadcaster Sportitalia, Roma’s Olsen is one of them.
The Merseyside-based club are in talks with the Italian Serie A club over what could be a loan deal for the 30-year-old goalkeeper.
Everton have also been linked with Spanish goalkeeper Pau Lopez, who also plies his trade for the Giallorossi.
Ancelotti’s side have also looked at the domestic market, with the club credited with an interest in Tottenham’s Paulo Gazzaniga and Manchester United’s Sergio Romero.
With a number of names of Everton’s list and limited time, it remains to be seen who the club will sign before the clock stops ticking.