The departure of Cortese, a very popular figure with manager Mauricio Pochettino and his players, was announced by the Saints on Wednesday evening and is believed to be the result of long-standing issues with Katharina Liebherr, the club's owner and new non-executive chairman.
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Shaw, widely regarded within the game as one of the most talented Englishman of his age group, has long been monitored by Tottenham and Chelsea, who view him as a potential successor to Ashley Cole.
And on hearing the news of Cortese's departure, the 18-year-old did little to quell the speculation surrounding his future by taking to Twitter to express his disappointment.
"Gutted with that news, but would just like to thank Nicola Cortese for everything he has done for me and the club! All the best to him!," he wrote.
Announcing the news of Cortese's resignation, Liebherr stated: "With great regret we have accepted the resignation of Mr Cortese.
"He [Cortese] has done a wonderful job and we very much wanted him to stay. A search has now begun for a successor.
"It is business as usual and we will ensure that the manager, team and staff at the club have all the help and support they need."