The Blue’s midfield legend is in the last year of his contract at the club and new manager Rafa Benitez has revealed the player will be free to leave Stamford Bridge at the end of the season.
Signing Lampard, 34, would be going against Wenger’s usual preference of looking to sign and develop stars for the future rather than those who have already reached their peak.
Lampard has been subject of rumours linking him with a move to LA Galaxy but the England international is reported to be keen on staying in Europe.
With the midfielder able to move on for free in the summer, Wenger will be weighing up the decision of whether to make a cash offer to Chelsea for him in January in a bid to prize him away early.
Arsenals miserable start to their Premier League campaign sees them in 10th position in the table and Wenger has fallen under increased pressure to turn the clubs fortunes around.
The Frenchman has also been heavily linked with moves for strikers Klaas-Jan Huntelaar of Schalke, and Atletico Madrid’s Adrian Lopez, as well as Everton midfield Marouanne Fellaini amongst others.