The in-demand midfielder has also been linked with a move to Liverpool's Premier League rival Arsenal but looks set for a switch to Anfield, with Rodgers hopeful that a deal is imminent.
It is believed the biggest hurdle to Sahin's mooted move to the Gunners is Arsene Wenger's insistence on an option to buy the player at the completion of the loan deal.
Real Madrid coach Jose Mourinho is also reportedly keen on sending his player to work with Rogers.
"Hopefully in the next 24 hours we will get some confirmation on that. It's quite far along. He's a very good footballer," Rodgers said.
Speaking after his side's 1-0 win over Heart of Midlothian in the UEFA Europa League, Rodgers played down the absence of striker Andy Carroll from the match, citing a hamstring problem.
Carroll failed to make the squad for the play-off first leg in
However, Rodgers says the forward was set to start against Hearts and he remains hopeful he will be fit for this weekend's visit of champion Manchester City.
He said: "Andy was due to start. He had a slight twinge on his hamstring.
"We had a scan on it and it didn't show a tear, just a slight disruption.
"We tried to give him 48 hours, let him travel and he trained yesterday to see how it was.
"It was still a bit tight and the medics' advice was it was too much of a risk for him to play.
"It was unfortunate because he has worked well and I know he was desperate to play.
"Hopefully missing the game tonight will allow him to recover for the weekend."
An own goal from Andy Webster with 12 minutes to go was all that separated the two sides and Rodgers refused to concede the outcome of the tie is now a foregone conclusion in the second leg at Anfield next week.
He said: "We always respect every opponent. We're not that good to be that complacent to be honest.
"We've got an awful lot of work to do but I was delighted for the players tonight.
"Once they got the positioning right in the second half, they were excellent at times.
"It was great for me to see some of the players who haven't been playing so much, some of our young talent as well.
"All round it was a good win and another clean sheet, which is important."
Hearts boss John McGlynn felt the outcome was harsh on his players.
He said: "I think the least we deserved was a draw. The players' effort, discipline and the way they went about the game deserved a draw.
"It was a bit cruel to lose the goal in such a manner as well. It was a cruel blow.
"There were a lot of positives to take from the Hearts team tonight."
On next week's clash at Anfield, he added: "It's only 1-0 so you never know.
"We've got another game on Sunday against Aberdeen so if we can put in a good performance and get a good result, we would go down to Anfield with confidence.
"We are kind of out of it so we've got nothing to lose."
UEFA Europa League
Changes to Champions League rules could see