Rodgers' side are 14th in the Premier League after winning only one of their opening seven matches but Sahin can see a comparison between the Liverpool manager and Borussia Dortmund boss Jurgen Klopp, who took over a side in the doldrums and turned them into domestic champions.
Dortmund had just finished 13th in the Bundesliga when Klopp arrived in 2008, but he guided them to the league title in 2011, and they retained it last season. Sahin, who played in the 2011 title-winning side before moving to Real Madrid, is certain that Rodgers can have a similar impact on Merseyside if he is given time.
"It will take time to take Liverpool back to where it wants to be," Sahin told Liverpool FC Magazine. "When Klopp came, we did not have a squad to be champions. He changed a lot, bringing his own philosophy in. It took a while for everybody to follow it.
"He had to be calm and consistent. If you go on this way, in the first two or three weeks, OK, you might not get the results, but in the long term it will go your way if you don't change it. The club gave Klopp the time to do this and it worked out very well. But as a character he is a person who relates to the player.
"I can see Brendan doing the same. Brendan's character was very influential in me coming here."
Meanwhile it has emerged that Liverpool paid Swansea £5 million to take Rodgers and his backroom staff to Merseyside in June.
The figures, published in Swansea's annual accounts, show that the compensation figure was paid to bring in Rodgers, his assistant Colin Pascoe, head of performance Glen Driscoll and match analyst Chris Davies.