Meirless sustained a knee problem against West Ham last weekend.
“We’re hopeful,” Clarke told Liverpool’s official website.
“He had a little problem with his knee and as a precaution at the start of the second half we thought it was better to take him off.
“That gives him a better chance of being ready for the next game.
“He’ll get three or four days on the easier list and then hopefully towards the end of the week we’ll be able to put him back in the preparations for the weekend.”
Clarke said of Agger and Aurelio: “They are both on the easy list at the moment and we’re almost sure Fabio Aurelio will join us (in full training) on Thursday, and we’re hopeful Daniel will join us on Thursday or Friday at the latest.”