Meireles hobbled out of last weekend's defeat at West Ham in the early stages of the second half but Clarke has revealed that the substitution was only a precautionary measure.
"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."
Aurelio could be available to face United as the Brazilian is expected back in full training before the end of the week after recovering from an adductor injury.
Agger is also set to return. Clarke said: "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."