Pardew revealed on Friday that the club have received approaches for the 30-year-old but that none had met the Baggies' valuation of the player, who has 18 months left on his contract.
The former Manchester United man was instrumental in his side's impressive 3-2 win at Anfield but was clearly struggling towards the end, and Pardew has suggested it could affect a possible transfer in the final few days of the window.
"Jonny is being approached by big clubs," he told BT Sport . "As yet, we haven't got an offer that's right for a player of his quality, which he showed tonight.
"He was playing with what looked like a hamstring [injury]. We'll have to wait and see but that might affect that decision.
"That's what the window is about – it's a moving feast and you have to react."
City were linked with Evans in the previous transfer window, too, but their reported interest in signing Aymeric Laporte for €65million has quietened talk concerning the West Brom captain.
Arsenal are believed to be the most likely destination if he leaves the Midlands, although manager Arsene Wenger on Thursday stressed the Gunners are "not close to signing anyone" .