Carroll left St James' Park for Liverpool in a big-money move in January 2011, but failed to make an impact on Merseyside.
The 25-year-old scored only six goals in 58 appearances before being loaned out to West Ham and signed a permanent deal with the London club last year.
Gateshead-born Carroll has been plagued by injuries during his time at Upton Park, but came through 90 minutes in a 2-1 Premier League defeat at Everton last weekend.
The big frontman will be hoping to keep his place when Newcastle travel to the capital on Saturday to face West Ham and Pardew would not be surprised to see him make a move back to Tyneside before he ends his playing days.
Newcastle boss Pardew said: "I think he would [want to come back to Newcastle], and I hope he does come back to his home town. He has got that love here. I really enjoyed working with Andy.
"I think he's a terrific player. I know we get linked with him every two weeks, which is always probably going to happen whether it's me or another manager.
"So I'm not going to hide from the fact that I like him. I think he's a good player. I'm pleased that he's fit and not injured, as that's been his biggest problem since he left us.
"I'm not sure that it's something that's imminent for us in this window, because he looks fairly happy to me at West Ham.
"I think it's difficult to take players who are happy out of Premier League teams. It's financially difficult."
Newcastle will be aiming to stretch their winning run to seven games in all competitions when they face Pardew's former club West Ham this weekend.
