The 22-year-old, who joined from Arsenal in 2012, spent the first half of the season on loan at Championship side Birmingham City before returning to South Wales to feature just three times in all competitions.
Bartley did start in the final day win over Sunderland, though, and he admitted that he is keen to stay beyond his current terms despite being yet to establish himself in Garry Monk's side.
"I'm really happy with the manager coming in and I've got a year left on my contract," he told the South Wales Evening Post.
"With Garry and the chairman, I'd like to look forward to the future. I'd like to extend my contract if that's a possibility. In the next couple of days we'll all sit down together and see what the future holds.
"I haven't played as many games as I wanted to since coming to Swansea, but at the same time I've got to look at my age.
"I'm only 22, so I've got a lot of time ahead of me and a lot of things to work on.
"That's all I'm focused on. It's a new season in a couple of months and hopefully I can hit the ground running."