Tevez had been expected to leave the Etihad Stadium in January, but after seeing potential moves to Inter Milan, AC Milan and Paris Saint-Germain fall through in recent weeks the Argentine forward could be forced to remain with City until the end of the season.
Reports from both the Guardian and Sky Sports claim that Liverpool made an audacious move for the striker by offering Andy Carroll in a straight swap deal.
Carroll joined Liverpool from Newcastle last January in a £35million deal but has failed to impress as yet at Anfield, with just six goals to his name for the Reds.
It is understood that City have rejected Liverpool’s advances and are holding out for a straightforward £30million cash deal for Tevez.
Rangers have been handed a boost ahead of the Old Firm derby at Ibrox on Sunday after Alfredo Morelos signed a new deal that keeps him at the club until 2021.