Boruc joined the Saints on a free transfer in September, but his current deal at St Mary's expires in the summer.
The Poland international has turned his reputation around on the South Coast, having gone from throwing a water bottle into the crowd after receiving criticism to saving a last-minute penalty against Norwich City on Saturday, and he admits that he wants to keep on improving.
"I will leave it to my agent and the club," Boruc said. "I am just doing my best and I'm working hard, so we will see what is going to happen.
"It's always important not to lose. We are working hard and I think we have shown in the last couple of games that we can play good football.
"We don't look like a team who should be relegated and that's the main thing. We are quite confident. I think it's a matter of time and we are going to grab points."
Boruc spent five seasons at Celtic, ending in 2010.