Lampard is considered the leading candidate to succeed Maurizio Sarri, who left Stamford Bridge on Sunday to take over at Juventus after just 11 months in West London.
The Blues’ leading all-time scorer has only one season of managerial experience under his belt, coming at Derby County last season, but The Sun claims that Chelsea are serious about putting him in charge.
Abramovich is rumoured to have invited Lampard to join him on his £380m yacht off Saint-Tropez, near where he is currently holidaying.
Chelsea will reportedly offer a three-year contract to Derby County manager Frank Lampard later this week.
The Blues legend is the overwhelming favourite to replace Maurizio Sarri, who has departed Stamford Bridge to take over at Juventus.
Derby are keen to keep the 40-year-old in the East Midlands, which has allegedly led to the former England international being offered a new deal.
However, ESPN claims that the Blues are ready to make a formal approach for Lampard, presenting their ex-midfielder with the chance to commit his future to the West Londoners until 2022.