The Magpies launched an audacious cut-price bid to recapture the 23-year-old, who they sold to Liverpool for £35m in January 2011, when it became obvious he had little future at Liverpool under Brendan Rodgers this summer.
However, the Merseysiders loaned the player to West Ham, with whom he will return to St James' Park tomorrow.
But as he prepared to welcome the 6'3" striker and midfielder Kevin Nolan back to Tyneside, Pardew revealed that he had not given up hope of clinching a permanent deal for the former.
He said: "He's a Liverpool player and not wanted so at some point he's going to move permanently. I'd like to think we'll be in the mix for that."
Indeed, Pardew revealed he would happily take both men back if the financial side was right.
"Big Andy hopefully one day will want to come back and certainly I'd like to have them both in my squad now because we would be stronger for it. But obviously finances restrict me from doing that."
Pardew had earlier admitted Carroll's "astronomical" fee had paved the way for the club's recent success.
There was fury in the city when Carroll moved to Anfield.
"The position we are in is because we used the money from Andy's sale well," Pardew said. "He was a brilliant player for us, but the fee was astronomical. We have used it well and we owe a great debt to him.
"It's nice to see Kevin come back. He did a super job here. And he has proven that at any level, he will get a goal."