
The Reds offered to pay a larger proportion of the 23-year-old's £115,000 a week wages, swinging the deal in their favour.
Sahin, who has 31 caps for Turkey, will undergo a medical ahead of the match against Manchester City on Sunday.
Arsenal manager Arsene Wenger is now considering a number of other targets.
Sahin had been expected to join Arsenal, having privately expressed a preference for the north London club.But the deal stalled when Real and Arsenal could not agree a £14m option to buy the player at the end of the...