Earlier this week, the Blues legend told talkSPORT of his plans to enter management. (Full interview here)
He has been studying for his coaching badges and has spent time working with young players at Chelsea's academy.
Now, according to The Sun, Roman Abramovich wants the 39-year-old to return to the club on a full-time basis and take up a senior coaching role.
There are doubts over the future of manager Antonio Conte but Abramovich is understood to want Lampard in regardless of who is in charge next season.
Abramovich reportedly sees the club's record goalscorer as a future Chelsea manager and is eager for him to work alongside an experienced manager first before potentially taking the top job.
Carlo Ancelotti and Luis Enrique are the frontunners to replace Conte should he exit Stamford Bridge in the summer and Lampard would not have an issue working with either man.