RB Leipzig coach Julian Nagelsmann has admirers in the Blues boardroom, but there are concerns over whether he would leave his current employers mid-season.
That would pave the way for Tuchel to be appointed now and he could be in charge for their home game against Wolves on Wednesday night.
Lampard pictured with his wife Christine out for lunch in Knightsbridge, London in October
The dismissal of Lampard will mean another pay-off for owner Roman Abramovich with Lampard earning £4million a year. His contract ran until 2022.