The English forward played alongside Lennon during his playing career, and the pair were part of the Hoops' treble-winning side at the turn of the Millennium.
And now the Celtic boss is keen to reunite with his former colleague.
Johnson is currently working at Nottingham Forest but could be persuaded to join forces with Lennon, according to the Daily Mail.
Celtic are still hoping to bring in a number of new players before Monday's transfer deadline, and recruitment chief Nicky Hammond is working hard on options.
Red Bull Salzburg left-back Gideon Mensah is mulling over an offer from the champions, according to reports in Ghana, while there is still uncertainty over Celtic's interest in Birger Meling and Greg Taylor, with Sunderland entering the race for the latter.