Sky Sports understands that Pochettino is in talks with Tottenham Hotspur about succeeding Tim Sherwood.
And Clyne is quick to admit that Pochettino has played a huge part in his progress over the past 12 months.
"For me personally it took my game to another level. It would be a real shame if we were to lose him," Clyne told the Daily Mirror.
"He has been so different to any other manager. He planted it into our heads that even if we were up against bigger teams and bigger players, we could compete at the same level as them.
"He taught us never to fear them or be intimidated just because of their big names or their big reputations.
"He'd have us pressing high, keeping a high line, receiving the ball in difficult situations, keeping possession and basically having the confidence to play football rather than being afraid.
"The understanding in our defence was down to our training. We worked really hard on our fitness and our intensity and it showed in the games."
Clyne himself is one of a number of Saints players being linked with big-money moves this summer.
"It's always flattering to know that big clubs are looking at you. Its shows that you are progressing as a player and that you are being recognised for what you are doing on the pitch," he said.
"I guess the dressing room has been a bit on edge. No one really knows where their future lies. Whether they will be back next season or not.
"But it has also made the players perform better, knowing there has been people watching us and with a World Cup around the corner. People have been trying to get into the England squad for it. I'm sure it has actually helped."