Lampard is of course out of contract with the Blues in the summer and is allowed to talk to clubs in the January transfer window.
This has caught the attention of Gunners boss Arsene Wenger and he could make an exception to his usual transfer policy, which is signing young players that he can mould into superstars.
Wenger may have a decision to make as to whether to sign Lampard in the January window, or wait until his contract runs-out at Stamford Bridge and try to land him on a free in the summer.
The 34-year-old is unlikely to get a new deal with the club where he has become a legend and the North Londoners making a move for him would certainly be a massive surprise.
However, Lampard is considered one of the best midfielders in the English Premier League, even at 34 and his fitness does not seem to be a problem at all.
He could be just the kind of player that Arsenal need to reignite this poor campaign they are having.
Would the Chelsea man move to the north of the capital?
We shall see.