The Dutchman was signed by former boss Ronald Koeman in the summer for £25m.
But his Toffees career failed to ignite and he is still yet to score or even provide an assist for the club.
Klaassen has been unceremoniously dumped from the match day squad by Allardyce as the former England boss has revived their season.
The 24-year-old, who has 16 caps for the Netherlands, has not played a Premier League game for Everton since September.
And Allardyce explained that Klaassen has been made aware that he must leave the club either on loan or permanently.
“Because he has never appeared on the subs bench it would be better benefit for him and the club if he moved on just on loan,” Allardyce said.