Argentina international Tevez is widely expected to leave the Etihad Stadium during the January transfer window having been AWOL in his homeland since November, a move which has cost him a staggering £9.3million in lost wages and incentives.
AC Milan, Inter Milan and Paris Saint Germain have all been linked with his services at various points throughout the past month, but a deal to end his spell at City appears no closer to being concluded.
Now Liverpool are understood to be the latest side to make an offer for the former Manchester United and West Ham man, offering misfiring forward Carroll in return.
The £35million signing from Newcastle during the January transfer window last year has failed to sparkle on Merseyside, scoring just six goals since his arrival with the Anfield giants.
However, the Reds' offer to their Premier League rivals is believed to have been rejected by City, with Tevez also not interested in the short move from Manchester to Merseyside.
Roberto Mancini's men are believed to be holding out for what they regard to be the full market value for their former captain, and will only sanction a deal if they receive an offer of £30million.
With the transfer window due to slam shut on Tuesday night, there are sure to be further discussions behind the scenes by Tevez's advisor Kia Joorabchian as he looks to secure his client's long-term future.