The Gunners boss is looking to land a top-class striker with Kylian Mbappe also on his radar.
However, a deal for the Monaco star appears out of reach, even for Real Madrid.
As a result, Wenger is considering other targets and has a long-standing interest in compatriot Lacazette.
The Arsenal manager has subsequently met with Lyon president Jean-Michael Aulas this week to try and reach an agreement over a fee.
Lacazette has outlined his intention to finally leave the French outfit this summer, and described the Premier League as an 'interesting' prospect.
Alexandre Lacazette is set to leave Lyon with Arsenal, Liverpool and Manchester United in the hunt
[Arsenal] have stepped up their pursuit in a bid to close a £50million deal
Despite Arsenal's failure to qualify for the Champions League, the goalscorer has not closed the door over a move.
And according to The Sun, the north London club have stepped up their pursuit in a bid to close a £50million deal.
That would make Lacazette Arsenal's record signing, with Arsene Wenger ready to spend big this summer.
Alexandre Lacazette odds: Who will sign Lyon star? Fri, June 2, 2017
Alexandre Lacazette has been linked with a big money move but who will sign the Lyon star?
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He is apparently sure he can attract the Lyon hitman to the Emirates with the promise of a contract worth £200,000 a week.
Wenger and Arsenal chief Ivan Gazidis were spotted at Nice airport this week.
Despite being close to Monaco, it is claimed Wenger's visit was in regard to 26-year-old Lacazette, not Mbappe.