Mina, 23, has been made available for transfer by the Catalans after struggling to carve out a first-team place following a move from Palmeiras in January.
A strong World Cup showing, however, has meant that the talented centre-back has had no shortage of admirers so far in the transfer window.
While both Lyon and Manchester United have been linked to Mina, Goal understands that Barca and Everton have agreed a €32m (£29m/$37m) deal after a furious weekend of negotiations.
Still, Aulas insists that his club will continue their pursuit and is unmoved by the latest news.
"Farewell Lyon, Mina is going to Everton for €32 million... I don't think that information is accurate," the Lyon chief wrote on Twitter.
"Yerry is still very interested in l'OL. We also want him to come to Lyon so he can play the Champions League."
Lyon, who finished third in Ligue 1 last season behind Paris Saint-Germain and Monaco to reach the Champions League, have made little impact on the transfer window this summer.
But with Nabil Fekir widely expected to leave and having lost defender Mouctar Diakhaby to Valencia, Aulas is keen to reinforce his team before the Ligue 1 season resumes this month.