However, Cortese, who left his role in January, has claimed that he did not receive any indication that players wanted to leave during his time at St Mary's.
"We created those talents," Cortese told BBC Sport. "It was key to keep them. You don't produce them just to sell, otherwise you give away your ambition.
"I was confident about plenty of conversations I had with the players. 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."
The future of manager Mauricio Pochettino also remains up in the air following reported interest from Tottenham Hotspur.