The Magpies boss believes the striker and midfielder Kevin Nolan, both currently at West Ham, would significantly strengthen his squad if they were to come back to Tyneside
Carroll was sold to Liverpool during the 2011 January transfer window in an enormous £35 million move, but has fallen out of favour at Anfield under Brendan Rodgers.
The England international has since joined West Ham - who travel to St James' Park on Sunday - on loan until the end of the season, reuniting with fellow former Newcastle star Kevin Nolan.
And Pardew has confessed he would be interested in bringing both players back to the club.
"He's a Liverpool player and not wanted so at some point he's going to move permanently," Pardew told reporters. "I'd like to think we'll be in the mix for that."
"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."
Since the sale of Carroll, Newcastle have signed the likes of Papiss Cisse and Yohan Cabaye and secured Europa League football, which Pardew believes is largely due to the money made from the striker's move to Anfield.
He said: "The position we are in, if I'm honest, is because we used the money from Andy's sale well.
"He was a brilliant player for us and we owe a great debt to him."