Gajan, who was axed by Bayonne earlier this season with the side struggling in the Top 14, has been mooted as a potential replacement for the Welshman but Melegari insists there is no foundation in these rumours.
"I have already told the coaching staff, including the director of rugby not to start worrying about their futures," said Melegari.
"It's true, our financial problems are well known. What happened the other day confirms there's something strange going on to destabilise us. It's not possible that in the space of ten minutes I was phoned by three national papers to ask whether it's true that I was thinking of replacing Rowland Phillips with Christian Gajan.
"While we're happy with how things are going in the RaboDirect PRO12 with the three home wins, the return in the Heineken Cup has been negative.
"In the first place the players haven't yet given the right response. And, I repeat, I expected more support especially from the more experienced players who have been up and down, as has been shown with the RaboDirect PRO12 wins against Treviso and Connacht.
"On the other hand Clermont, like Leicester have a budget which is three or four times ours. Munster, Leinster and the Ospreys in the PRO12 have budgets at least double ours, and more foreigners."