"Southampton is my baby I'm not going to abandon it," Cortese said.
The Swiss-Italian confirmed he was aware of the interest but remains focussed on delivering success to Saints owner Markus Liebherr.
Cortese added: "I'm a friend of Markus. It could be tempting but I'm not driven by money and people who work with me on a daily basis know that.
"I talked him [Markus] into this and he keeps reminding me of that.
"He said at the time 'I will only do this project if you will be on board' and that remains the case."
Source: BBC Sport
Source: BBC Sport