The 23-year-old England international's future has been a topic for debate ever since new Reds manager Rodgers hinted that he may not be part of his plans, prompting the Magpies to launch a bid to bring him back to Tyneside, initially on loan, and then permanently for a fraction of the £35million for which they sold him.
Pardew told BBC Radio Newcastle: "[Reading chairman] John Madejski used to say to me about certain players, 'Just wipe your nose and move on', and I think [Liverpool] are going to have to do that with Andy."
Liverpool have insisted Carroll will not be allowed to go out on loan and are understood to be holding out for around £20million with West Ham and Fulham also having been linked with the Gateshead-born frontman.
But Pardew added: "I think it was obvious as soon as Brendan went into Liverpool that Andy's time was going to have to be somewhere else. 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, Newcastle owner], 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."
Part of the fee Newcastle received for Carroll was used to replace him with Demba Ba and Papiss Cisse, who scored 29 goals between them last season, while Shola Ameobi also played an important part in the club's fifth-placed Barclays Premier League finish.
They have been linked with a series of striking targets this summer including Carroll, Luuk de Jong and Loic Remy, but the position is complicated by a release-clause in Ba's contract.