Lampard has two years remaining on his contract at Pride Park and it would require a fee of £4m to take him away from the Championship club.
Chelsea now can not recruit a replacement with the club serving a two-window transfer ban handed down by Federation Internationale de Football Association.
The amount of compensation for Sarri held up his return to Italy but the problem appears to be overcome with Chelsea expecting to receive in excess of £5m.
The goal-scoring midfielder would be well placed to work with Chelsea's crop of talented youngsters then, who would likely be handed extra first-team chances should that transfer ban be enforced.
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Former Chelsea boss Glenn Hoddle believes it is the "right time" for Frank Lampard to step into the hot-seat at Stamford Bridge.
Terry and Lampard were pillars of Chelsea's success, but it doesn't look as if Lampard will call on his old team-mate should he become Sarri's successor.
"I think he's going to rub up against certain characters at Juventus, and his tactical dogmatic nature is going to be hard when you've got so many talented players to make use for".
"(Eden) Hazard has gone, if the transfer embargo is there for two windows, it is going to be a real balancing act, and a really experienced manager would find it hard".
The ex-Chelsea man would jump at the chance to manage his former club I'm sure, but, having just lost their best player in Eden Hazard to Real Madrid and now being under a transfer embargo, perhaps this might be a fairly hard time to take the reigns.
Cristiano Ronaldo is understood to have given his blessing for Sarri to succeed Allegri at Juventus.