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The youngster has been linked with a switch to the Premier League heavyweight, which has presided over a high-spending January transfer window.
France youth international Gusto is the latest to be touted for a move, and has reportedly already agreed personal terms on a six-and-a-half-year deal.
But reports also said Lyon knocked back a £17.6million (€20m) offer from the Blues on Thursday, and Aulas has claimed the 19-year-old will not be going anywhere this month.
"I have the pleasure to explain that Malo Gusto, one of Lyon's big talents, will continue to play for Lyon until at least June 30," he wrote on Twitter.
Gusto is out of contract at the end of next season with the Ligue 1 outfit, who currently ninth with just one win from their last five top-flight matches.
The club reportedly value him closer to £35m (€40m) and may well be playing hardball in order to convince Chelsea to either up their offer or wait for the end of the campaign.
With 47 appearances for his hometown club, Gusto is already knocking at the door of the France senior team under Didier Deschamps.
If he was to move to Chelsea, he would become their seventh arrival of the transfer window, and second from Ligue 1 after Monaco defender Benoit Badiashile.
David Datro Fofana, Andrey Santos, Mykhaylo Mudryk and Noni Madueke are the other permanent arrivals at Stamford Bridge, while Joao Felix also joined on loan from Atletico Madrid.