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.
However, Rodgers said: "I don't look beyond the loan period because there are lots of things which will determine whether he ever came here (permanently)."
He added: "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 Sahin 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."
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."