Chelsea are set to replace Maurizio Sarri with this manager
Sarri endures a difficult relationship with Chelsea supporters despite leading the team to two cup finals and a third-place finish in the Premier League this season.
The Italian could therefore depart Stamford Bridge even if the Blues beat Arsenal in the Europa League final next week.
Juventus are on the lookout for a new boss and are reportedly keen on Sarri.
And Chelsea will turn their attention to former midfielder Lampard, who is one game away from taking Derby into the Premier League, if Sarri leaves.
Lampard masterminded the Rams' victory over Leeds in the Championship play-off semi-finals but would presumably find the Chelsea job too good to turn down even if his current club book their place in the top flight by beating Aston Villa next Monday.