Butler has not played under Rodgers since joining the club as he is still to recover from a ruptured thigh muscle.
However, he is now hoping to be back playing for the Swans in February and helping their push for promotion.
Butler told the South Wales Echo: "It's the last year of my contract and that is something which would spur a lot of people on.
"But it's out of my hands in a way. I've been out of the team for quite a while and the clock is running down, but my main goal is getting fit and making myself available.
"I've missed out while the other lads have been given opportunities, so I want to make a big impression on him when I finally return."
Source: PA
Source: PA