Pochettino has been linked with the managerial vacancy at Tottenham, and left-back Luke Shaw and captain Adam Lallana - both in England's World Cup squad - have been subject of reported bids from Manchester United and Liverpool respectively.
Cortese, who resigned in January, told BBC Sport: "I don't know what has happened since I left, so it is difficult for me to judge whether he (Pochettino) potentially wants to leave or whether the offer from another club is really that good.
"But he is ambitious and rightly so
When you plan a career, it is important to make the right decision at the right time.
"Often we have maybe seen people take too quick a step which ultimately backfires.
"But he has to make his own decision
He is a young manager
He has plenty of time to have a great career."
Cortese joined in 2009 when Southampton were in League One and appointed Argentinian Pochettino as successor to Nigel Adkins in a move which was initially unpopular but has since been seen as justified as Saints climbed the Barclays Premier League standings.
Cortese had enquiries but no formal offers for Southampton's talented aces while in charge, but the squad could unravel this summer.
England striker Rickie Lambert, Croatia defender Dejan Lovren and French midfielder Morgan Schneiderlin have attracted admirers along with Lallana and Shaw.
"We created those talents," Cortese added.
"It was key to keep them
You don't produce them just to sell - otherwise you give away your ambition.
"I knew the players themselves wanted to stick together because this vision was something they believed in, too
I didn't see any reason for them to go."
Source : PA
Source: PA