Tremmel is currently being given an extended run in the Swans side, having started five of their last seven games, with number one keeper Michel Vorm in and out of the team through injury.
The Dutchman is now being sent for an operation on his knee and will be sidelined for two months, leading to speculation that manager Michael Laudrup will recruit some temporary cover between the posts.
He has been linked with a loan move for out-of-favour Aston Villa keeper Given, who is currently on a short-term deal at Championship side Middlesbrough, and Tremmel would be happy to see him join the Welsh outfit.
He told The Sun: "I welcome any competition. With Michel out we are very tight, although we have two young talented keepers.
"I'm always happy when I'm playing and always try my best. I just want to give the team as much as possible - but, of course, I have one eye on myself.
"It's even better when I have a few games in a row because you can get into a rhythm. Everyone wants to get confidence so you can show your best on the pitch."
Given, 37, has made a total of 440 Premier League appearances over 12 years at Newcastle United, and spells at Manchester City, Villa and Blackburn Rovers.