Liverpool have made a remarkable bid to swap Andy Carroll with Carlos Tevez and move on their club-record £35m signing not even a year after signing him from Newcastle United.

The Anfield club contacted City on Thursday to ask how much they want for Tevez and whether they would be willing to contemplate a straight exchange with Carroll. Brian Marwood, the City football administrator, rebuffed the idea immediately, even though Carroll is a player Roberto Mancini has admitted admiring when he was at Newcastle.

The move demonstrates how Liverpool are now openly looking at offloading Carroll despite the insistence behind the scenes at Anfield that he can still play a prominent part and Kenny Dalglish's praise for the player after the 2-1 FA Cup defeat of Manchester United.

Carroll has scored only six goals in 35 appearances since becoming the eighth most expensive footballer in history and has not even been able to establish himself as a regular starter this season.

His problems adapting on Merseyside have also left Liverpool willing to take a £10m hit on the player, with Tevez valued at £25m, though that revelation is hardly surprising considering his difficulties at Anfield, added to the sense that he has not always been fully focused.

Fabio Capello, the England manager, has already expressed misgivings about the lifestyle of a player who has managed only two league goals this season in 20 appearances.

Those remarks went down badly at Anfield, with Dalglish defending Carroll, but the questions will probably not go away until he becomes a regular scorer. Carroll's longest run of starts this season is three games and Marwood's decision was made on the basis that he could no longer improve their team even though Mancini has a shortage of front players at a time when Tevez's strike is in its 11th week and Mario Balotelli is now serving a four-match suspension.

Tevez is planning to return to Manchester next week now it has become apparent that Milan are not able to meet City's asking price and, unless anything changes before Tuesday's transfer deadline, his adviser, Kia Joorabchian, says the Argentinian wants to re-establish himself in the team.

Whether that is possible remains to be seen, with Mancini not prepared to entertain the idea unless there is an apology from Tevez for walking out on the club and the string of other offences that have already led to him being found guilty of gross misconduct and losing almost £10m in wages, fines and lost bonuses since the start of the season.

Tevez is still a formidable striker and finished as the league's joint-top scorer last season, but he will be returning to England with a severely damaged reputation and Liverpool's attempt to take him along the M62 will surprise many people given his propensity for causing dressing-room problems and an apparent dislike of living in England.

There is also the fact that, approaching his 28th birthday, he would not have fitted into Liverpool's usual policy of buying players at a young age who will keep a resale value over the course of their contract. Liverpool, however, were willing to make an exception and City would have been glad to arrange a deal after unsuccessful talks not just with Milan but also Juventus, Internazionale and Paris St-Germain. They remain open to offers for the Argentinian but will not change their mind about Carroll.