The pair have featured just 12 times between them in the Premier League in their debut campaigns at Goodison Park, seeing playing time further restricted since Allardyce arrived in November.
Allardyce has made clear that he intends to cut the size of Everton's playing squad in the remaining days of the January transfer window, which could mean allowing Sandro and Klaassen to depart on temporary deals if the right amount is offered.
"We've had a number of enquiries that are not suitable for us to allow the players to leave, nearly all of them on loan," he told reporters at a press conference ahead of Wednesday's meeting with Leicester City.
"We haven't accepted any deal yet and we won't until the board tell me financially it's acceptable and I say to them it's in the best interests of the club or the player to go out on loan. We have got a lot of players so moving some out on loan would be a possibility but only if it's right for the club."
Everton have sold Ross Barkley to Chelsea and Aaron Lennon to Burnley so far this month, while Kevin Mirallas is one of four players - the other three being youngsters - to have been sent out on loan.