Everton defender Brendan Galloway has not played at all since Marco Silva arrived.
Klaassen left Everton in the summer after failing to make an impact.
Premier League outfit Everton drew 1-1 with Barnsley in the Checkatrade Trophy on Tuesday night.
Everton Under-23 drew with Arsenal 0-0 on Monday night.
Morgan Feeney, compared to Liverpool great Jamie Carragher by Martin Keown, was in action for the Everton Under-23 side against their West Ham United counterparts on Monday.
Everton signed highly-rated Portuguese goalkeeper Joao Virginia from Arsenal and he has impressed David Unsworth.
Fraser Hornby scored for the Everton Under-23 side against their Tottenham Hotspur counterparts this past weekend.
Josh Bowler joined Everton in the summer of 2017 after leaving Queens Park Rangers.
Ryan Astley may be just 16 but he has impressed for Everton's U23 side, so could he make his Premier League debut this season?
Everton's under-23 side were beaten 1-0 by Derby County, and David Unsworth could only pick out two performances that he was happy with.