The former Arsenal transfer target continues to serve his 10-game ban for biting Branislav Ivanovic, but is looking to maintain fitness against Port Vale at Melwood
Goal revealed on August 23 the 26-year-old is resigned to remaining at Anfield for one more season after the Reds owners made it clear he would not be sold, despite the player's public admission that he wishes to depart.
Liverpool rejected two offers from Arsenal for Suarez, the latter thought to be worth up to £42 million in a bid to trigger a supposed release clause after the Reds failed to qualify for the Champions League.
But Arsene Wenger has since admitted defeat in the chase, though Real Madrid are now reportedly interested.
Liverpool drew 2-2 with the recently promoted League One side, with Suarez still to serve three matches of his suspension.