The Emirates Stadium supremo has long been an admirer of the Belgian starlet - who has won 17 caps for his country - and is desperate to bring him to Arsenal, with Liverpool also believed to be tracking the talented youngster.
The 20-year-old has made more than 100 appearance for the Ligue 1 club after breaking onto the first team scene in 2007, scoring 12 league goals.
But with Lille currently sitting pretty at the top of the league in France, the Gunners' boss says he is happy to play the waiting game.
"He's a player that I have followed for some time, but I do not want to unsettle Lille now," explained Wenger.
"When he is available for transfer, we will see if there is the possibility to sign him."
Hazard's possible arrival in the summer could coincide with the departure of the Gunners' captain Cesc Fabregas, who was widely expected to leave Arsenal last summer for former club Barcelona.
The Gunners meet their Catalan counterparts in the Champions League next month, with Pep Guardiola's side tipped to renew their interest in Fabregas at the end of the season, despite the fact that they brought in Dutch midfielder Ibrahim Affelay at the turn of the year.
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