Saints manager Pochettino has been the subject of intense speculation on his future ever since chairman Nicola Cortese quit St Mary's in January.
Ex-Argentina defender Pochettino refused to guarantee he would stay beyond the summer when Cortese walked out of the south coast club.
Owner Katharina Liebherr has put a new board of directors in place since then though, and goalkeeper Boruc believes Southampton is "stable" enough now for Pochettino to commit.
"You can see that we've improved, we're playing very good football and it's enjoyable to see us play," said Boruc.
"That reward should easily be in the minds of the board and I think sooner or later it's going to happen.
"We'll see what's going to happen in the next few weeks, but I think it will happen soon."
Former Celtic and Fiorentina stopper Boruc said Southampton can help push Pochettino's new deal over the line by pulling out all the stops on the pitch.
Southampton take on Tottenham at White Hart Lane in Barclays Premier League action on Sunday, still pushing for the sixth-place finish that could secure Europa League football next season.
"We can try to convince the board by the way we're playing," said 34-year-old Boruc.
"That's all we can do, talking doesn't really do it, but we can help by playing well.
"We've just got to perform well in games and try to help him this way.
"I think it [a new contract for Pochettino] would be the sign of a stable club so you know, he's done lots of good things for this football club, and that's how it should be looked at."
Tottenham slumped out of the Europa League on Thursday night despite a high-scoring two-legged battle with Portuguese club Benfica.
Tim Sherwood has claimed that despite their exit, no one will want to face Spurs now as they start to find form.
Poland goalkeeper Boruc does not expect Spurs to suffer any fatigue from their midweek exertions, gearing up for a stern test in north London.
"We're professional football players and those kinds of things don't really matter," he said.
"You still have to train, a game has a bit more running, but in professional life it shouldn't have too much impact."
Portugal's management team have been tracking Saints defender Jose Fonte with a view to a potential World Cup call-up.
Boruc said his uncapped 30-year-old team-mate is more than ready for the step up.
"He's a good player and we're defending well as a team right now," said Boruc.
"So why not? It's more about the national coach than me of course, but I think he's good enough, he's playing in one of the best leagues."