The Gunners have made signing the France international their top priority ahead of the new campaign and are prepared to pay up to £44m to get their man - £6m more than they handed over to Real Madrid for Mesut Ozil four years ago.
Aulas appeared to play down suggestions on Sunday afternoon that a deal was close to being completed, denying reports in the French media that the 26-year-old had arrived in England to undergo a medical.
However, it has now been confirmed that negotiations are at an advanced stage with Arsenal and a transfer is nearly over the line, but the exact figure being paid for the prolific striker is not yet known.
"The transfer of Alexandre Lacazette to Arsenal could be done in one or two days," he told Le Progres. "We will probably reach a new record - it's not a small transfer, €50m for a player trained by our club.
"The first offer made by Arsenal was €45m. The deal will happen for something between €45m and €50m. The €67m announced by English sources and relayed was an impossible and not realistic sum."
Lacazette had his eyes set on joining Atletico Madrid this summer, only for the Spanish club to see their transfer ban upheld by the Court of Arbitration for Sport.
The former West Ham United target has scored 129 goals in 275 appearances for Lyon, 37 of which came during the 2016-17 campaign.