The 26-year-old was expected to join Atletico Madrid this summer, but the proposed move fell through when the Court of Arbitration for Sport upheld the club's transfer ban until January 2018.
Now Arsenal, who failed in their pursuit of Lacazette last summer, are reportedly prepared to spend £50m on taking the striker to the Emirates.
Lyon's recent acquisition of Bertrand Traore from Chelsea suggested that Lacazette's spot was being filled, but Aulas has insisted that no replacement has been found yet.
"Our position is that as long as we have not signed his replacement, we will keep him," Sky Sports News quotes Aulas as saying. "He expressed the wish to leave and he was given an agreement to go to the club of his heart, but things did not happen."
Since breaking into Lyon's first team in the 2009-10 season, Lacazette has scored 129 goals in 275 appearances.