The Real Madrid midfielder is due to undergo a medical at the club's Melwood training ground on Friday after manager Brendan Rodgers revealed the paperwork has been finalised
The Turkey international is expected to undergo a medical at the club's Melwood training ground on Friday, after terms were agreed over a season-long switch.
"We hope that will be complete. I believe from the club that everything has been organised and sorted in terms of paperwork. So we're hoping in the next 24 hours it can be done," Rodgers told reporters.
The Reds were previously believed to have given up hope of signing Sahin, following reported interest from Arsenal and the Madrid man's preference for a Champions League club.
However, it appears a last-minute change of heart from Gunners boss Arsene Wenger regarding a permanent deal at a later date has swung negotiations in the Merseyside outfit's favour.
And Rodgers praised his latest acquisition, adding: "He's a great technician. He was the player of the season in Germany and was the captain of Borussia Dortmund.
"He was fantastic at a very young age and got a move to Real Madrid and obviously through injury it hasn't quite worked out for him.
"He's a wonderful player technically and tactically, he understands the game and we hope that his extra bit of quality coming in will really help the group."