Chelsea is reportedly interested in the 23-year-old, who has scored 10 goals in Ligue 1 this season in 18 appearances, as Frank Lampard seeks a new forward to take some of the pressure off Tammy Abraham.
It has been suggested the Premier League club could offer cash plus Olivier Giroud to tempt Lyon into a sale during the transfer window.
However, Aulas insists Dembele wants to stay at the club at least for now, despite offers being made for some of Lyon's top players.
"Moussa Dembele will not leave because he wants to stay and win something with OL," Aulas said.
"There have been offers for him and for other players, but none of those whom we want to keep will leave in January."
Indeed, Aulas says Lyon's primary objective is to strengthen its squad and mount a challenge for the UEFA Champions League places, given it is 12th in the table after 19 matches.
"We'll try to make ourselves stronger," he said. "The first reaction was to get the youngsters in the academy to play more and show themselves more. The second is to recruit.
"The board of directors have decided to do that, but not at any cost and not in just any situation. We'll only carry out plans that correspond to what the sporting director, the advisers and the coach want."