The 23-year-old is keen to stay at Liverpool and prove himself to new manager Brendan Rodgers, but is coming to terms with the fact that he might not be required at Anfield.
However, with former club Newcastle and West Ham among the clubs to have been linked with him since Rodgers indicated that he could be surplus to requirements, Press Association Sport understands that the £35 million man is not prepared to move on anyone's terms but his own.
Carroll wants to stay and prove himself on Merseyside, but if he has to go, it will only be to a club which can offer him the lure of European action.
Newcastle, of course, can do just that following their fifth-placed Premier League finish last season, but the Hammers, who have reportedly made a club record bid, cannot.
Rodgers is beginning to remodel his squad and while he insists there is no chance of Carroll leaving Liverpool on loan, he admits the Reds will consider any offers they receive for the forward.
"There is talk of him going on loan, but there is absolutely no way I would be looking to loan a player like that, especially after the investment the club have paid," Rodgers said last week.
"But his condition will be the same as every player. If an offer comes in for any player at the club we would either look at it, or dismiss it, and Andy's no different to that."