The Hammers are reportedly ready to make a move for the midfielder, should they sell Scott Parker before the transfer window closes.
Nolan joined West Ham from the Magpies in June. Barton has been told he can leave Newcastle on a free transfer.
“Would Joey Barton come here? Well, I came here, so I can’t see why Joey Barton would not come,” Nolan told the Mirror.
“It is a massive club.
“The way he has been treated over the last couple of years, he is probably looking for an escape.
“He knows I’m here, he knows Sam [who signed Barton for Newcastle in June 2007] is here and what we are about – I can look after him and he can look after me!”
Nolan added: “It would definitely be good for me. Joey is a great player to play alongside and he is a winner.
“He tells it straight, as people know, but deep down he is a lovely lad and I get on really well with him.
“He would be a great acquisition to the squad if we got him here.
“I’m sure the West Ham fans would love him and the players would come to love him. They [will have] read a lot of things about him – some of them are true, but others are blown out of proportion.
“With Joey, you have got someone [who] when he puts on the shirt, he genuinely wants to win, and he wants to do the best for the club and the players.”