The Turkey international, who arrived late in August from Real Madrid, has taken a while to settle in but has scored three goals in his last two starts.
Sahin's improvement in form has come at the perfect time with Lucas Leiva still out injured and Jonjo Shelvey suspended.
But Rodgers insists it is still too early to make decisions on whether he wants to keep the 24-year-old or even whether Real Madrid manager Jose Mourinho would let him go.
"I don't look beyond the loan period because there are lots of things which will determine whether he ever came here (permanently)," said the Reds boss.
"One has to be availability. Jose (Mourinho) may decide after one year playing he is really the type of player he wants around his squad.
"Two: He might not be affordable. Affordability is important as well.
"We'd all love Lionel Messi but whether you can afford him or he's available is another thing.
"All I can concentrate on is Sa hin coming in here and helping him become the best player he can possibly be.
"If he finds he enjoys it here and he fits into the way we work, which I am sure he would do because he is a good guy and understands the game tactically and is prepared to fight for the club, then that is something come the end of the season we will talk about.
"But at this stage it is way too early. He is just starting to get up to speed fitness-wise but what he is is a real good guy and you have seen his performances.
"He has a wonderful left foot and the ability to score a goal and he was the captain of Borussia Dortmund at a very young age so he's got those natural leadership qualities."
Liverpool's current captain Steven Gerrard insists he is not thinking about his long-term future just yet but believes he can play on beyond his current contract.
The 32-year-old signed a new deal in January which runs until the end of next season but he does not necessarily see that as a natural finishing point.
"We will have to wait and see," said the midfielder at a golf event for his charity The Steven Gerrard Foundation.
"I'm enjoying my football, I feel physically strong, and I want to go on for a long time yet.
"I love playing for the club, I love being the captain. It's living the dream, so to speak.
"I'm enjoying playing under Brendan Rodgers. The training is good, it's a very exciting time, and hopefully I can continue to play and to contribute under the new regime."
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