Carroll who left Newcastle for Liverpool in January 2011, has been told he is up for sale by new Reds boss Brendan Rodgers and Newcastle are favourites to sign him.
Demba Ba scored 16 goals for Newcastle in his first season with the club, following his arrival from West Ham last summer.
An additional payment of around £10million could also be needed to push Liverpool into doing a deal, having paid £35million for his services less than two years ago.
The Northern Echo believes an offer including Ba has been made, with a number of Twitter sources supporting the rumours.
Carroll, despite claiming he doesn't want to leave Anfield, would find it hard to turn down a return to his boyhood club.