Lampard has spoken previously about his desire to manage Chelsea.
Chelsea have reached an agreement with Juventus that will see Muarizio Sarri take over as manager of the Italian side.
Gianluca Di Marzio further adds that it is Juventus Sporting Director Fabio Paratici who finalized the Sarri deal with Chelsea Executive Marina Granovskaia.
But there are still small issues to resolve and, according to Sky Italia, Sarri's representative has been holding talks with Chelsea this afternoon to finalise the termination of the manager's contract. However, following the issue of a looming transfer ban many observers felt he was safe.
Chelsea will be keen to secure a replacement well before the first senior players return for pre-season training in the first week of July, with Lampard high on their list of candidates.
There has been discussion whether Lampard, after just one season in charge of a club, is ready for the pressure of the Chelsea job.
Meanwhile, former Juve coach Allegri revealed on Thursday he intends to take a year off after leaving the Serie A champions.
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Conversely, Lampard might feel it is the wrong time to make such a big move - especially with the likely handicap of no summer signings and the vast chasm that already exists between Manchester City and Liverpool and the rest.
Although vastly inexperienced for the post, many Chelsea fans are backing Lampard to succeed Sarri, whose cyclical football masked last season's third-place finish and Europa League triumph.
Frank Lampard spent 13 years at Stamford Bridge, clocking almost 650 appearances and making a name for himself as one of, if not the greatest player in the history of the club.
Reports say compensation has been agreed between Chelsea and Juventus for Sarri, who won the Europa League last month, to leave.
Drogba continued: "Does he have to wait until he is 40 or 50 to be ready?"
"I think it is a very good option for the club", he said ahead of the Soccer Aid for UNICEF match at Stamford Bridge on Sunday.
It is elsewhere claimed he met with Chelsea earlier this week to discuss replacing Sarri.