The England international completed a £35 million switch from Tyneside to Anfield in January 2011 but it has been widely reported that new manager Brendan Rodgers is prepared to offload Carroll for the right fee.
Pardew has admitted that he would be pleased to see the 23-year-old return to Newcastle if owner Mike Ashley is able to complete a deal.
And the former West Ham United manager believes that both Liverpool and Carroll would benefit if they accepted that the move had not worked out as hoped.
"[Reading chairman] John Madejski used to say to me about certain players, just wipe your nose and move on," Pardew told BBC Radio Newcastle.
"And I think [Liverpool] are going to have to do that with Andy."
Newcastle have had one loan offer for Carroll rejected, with Liverpool reported to be holding out for a permanent deal worth around £20m.
Pardew thinks that the Gateshead-born target man will inevitably leave the Merseyside club eventually but acknowledged that he would not come cheap.
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"I think it was obvious that as soon as Brendan went into Liverpool that Andy's time was going to have to be somewhere else," he continued.
"I think it's quite right we're involved in that. Whether he comes here, is something that I will take or I will leave.
"It's a lot of money for Mike [Ashley], although we'll obviously be getting a big upside in terms of what we sold him for and we've got three great strikers here already.
"But of course as the manager I want the best players I can get."
Pardew also pointed out that while Liverpool may be forced to make a loss on Carroll, his sale would still bring in a considerable sum with which they could strengthen the squad.
"Whether it's £15m, £16m or £20m, if [Rodgers] uses that money and gets an uplift in the player that he brings in that's okay," he opined.
"And that's how you've got to look at it."