The 34-year-old will be out of contract at the end of the season, and speculation has suggested he will end his 11-year stay in west London.
Speculation over the weekend suggested the Gunners could make a shock bid to bring Lampard to the Emirates Stadium in January, with the England international making the short move across the capital from Stamford Bridge.
However, speaking to the press ahead of Arsenal's Champions League clash against Olympiacos in Piraeus this evening, Wenger made a joke about his connection to Lampard, referencing Greek philosopher Socrates.
"We are in the country of Socrates. He said, 'I know that I know nothing', and that is a bit like football," responded the Frenchman, when pressed specifically about plans to sign the Chelsea veteran.
Arsenal fans are desperate for Wenger to act in the upcoming transfer window, although rumours of a bid for Lampard have been met with a mixed reception, after the club's weekend defeat to Swansea City, which left them struggling in 10th place in the Premier League table.
The onus for now is getting the best out of the players that Arsenal have got, with speculation of what might happen in the New Year currently possessing very little importance.
"What is important now is to do well until 1st January," Wenger added. "What happens in January, we will see if we need to do something and we will do it."
Meanwhile, Lampard remains sidelined for Chelsea having not featured since he picked up a calf strain in the Champions League clash against Shakhtar Donetsk in October, but is working his way back to fitness to give interim Blues boss Rafa Benitez a lift ahead of the side's Club World Cup campaign later this month.