Everton have confirmed the incident, according to the BBC.
The site states that a masked gang broke in and stole jewelry and a watch from the family.
The British Daily Mail and The Sun report that Olsen, his wife and two children were at home when it happened.
"All the support they can get"
The robbers are said to have watched over Olsen's family while the Everton goalkeeper was forced to show around the perpetrators in the house.
Olsen is said to have handed over several valuables.
According to the BBC, Everton have communicated that they give Olsen and his family "all the support they can get".
The Sun states that the club has given all players their own bodyguard.
Investigate
According to the BBC and the Daily Mail, the incident is being investigated by police.
Several Premier League players have been exposed to similar crimes in recent times.
Just a few weeks ago, Olsen's coach Carlo Ancelotti was subjected to a burglary at his home in Blundellsands.
On Tuesday, Swedish national team captain Janne Andersson will take the national team squad to the World Cup qualifiers against Georgia and Kosovo and the training match against Estonia later in March.
SVT Sport has contacted Everton and Robin Olsen's agent Hasan Cetinkaya for a comment.
The Swedish Football Association does not want to give any comments but refers to Olsen's club, writes press manager Jakob Kakembo Andersson in a text message to SVT Sport.