Pochettino's future has been the subject of intense speculation ever since chairman Nicola Cortese quit St Mary's in January.
The former Argentina defender refused to guarantee that he would stay beyond the summer when Cortese walked out of the club, but Boruc believes that Southampton is now stable enough 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," the Polish goalkeeper told Sky Sports News.
"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."
Southampton take on Tottenham Hotspur at White Hart Lane, a club that Pochettino has been linked with in the last few days, on Sunday.