Club owner Massimo Cellino is also on the verge of a takeover at Elland Road after a successful appeal against a Football League ruling.
The news has fuelled reports that veteran midfielder Conti may be on his way to Leeds this summer, but he has dismissed the speculation.
"My future? We will talk later. Me at Leeds? I think no," he told Sky Italia.
Diego Lopez became the 36th manager to be fired by Cellino in his 22-year reign at Cagliari over the weekend, and there has been criticism of the club following a difficult season in Serie A.
However, they are seven points outside the relegation zone in 15th and Conti is proud to have spent the vast majority of his career at the club.
"I don't like it being said that with certain sides it is like driving a Ferrari, while here it is like driving an economy car," said the 35-year-old.
"I'm proud to be in this economy car for many years. This small car has stayed up for 11 seasons and there is a need to better respect the players."