The 26-year-old attacking midfielder starred for Lille last season, scoring 12 times in the league for the French club.
And Wenger has reportedly instructed his scouts to run the rule over the France international as he looks to strengthen his squad for next season.
Payet joined Lille from Saint Etienne in 2011 as a replacement for Arsenal-bound Ivory Coast winger Gervinho.
The Gunners wide-man is now thought to be surplus to requirements at the Emirates Stadium though, and reports have linked him with a return to Ligue 1.
In his place Wenger could look to sign Payet, who has three caps for France and can play on either side of a front three.
And the French winger enjoyed a sensational season for Lille last season. The club finished sixth in Ligue 1, with Payet directly contributing to a team-high 25 league goals.
He had 12 goals and provided 13 assists in 38 appearances. His 13 assists were the most in the league, one more than Marseille playmaker Mathieu Valbuena.
The report also claims Arsenal have made a £25m offer for Real Madrid forward Gonzalo Higuain. If accurate, the bid would shatter Arsenal's current transfer record.