Rodgers is in search of two new goalkeepers, with only new signing Jose Moreira and youngster David Cornell currently in the first-team squad. Tremmel, 32, has been training with the club and produced a sound 45 minutes after starting the win over the Hoops.
"We want to get players who can add to the squad and Gerhard did well," said Rodgers.
"He impressed me when he was with us in Austria and I liked his calmness and composure and, very importantly, his management of the game.
"With the way we play there will only be a certain number of keepers who can play how we play and fit in to that style.
"He played all of last season for Red Bull Salzburg and they play a similar sort of way, they try and build the game constructively from behind so he knows his passing lines.
"He has done very well and if I look at where we are at now, we have two signed keepers in Jose and David, but to allow David to go out on loan I need to bring in two other keepers and Gerhard could possibly be one of those with another one to come in."
Rodgers has also been pursuing Nottingham Forest keeper Lee Camp, although the east Midlands club have rejected Swansea's bids to date.
"I haven't spoken to the chairman," said Rodgers. "We have made a few bids and we will see how that goes over the next couple of days. He is a player we like but he is a Nottingham Forest player."
Source: PA
Source: PA