Sunday Times journalist Duncan Castles, is claiming that the two men had a phone call earlier this week and that the Derby County manager agreed to take up the soon to be vacant position.
Lampard sought assurances from Abramovich that he would be given at least two seasons at Stamford Bridge to make an impact and those assurances were forthcoming
Lampard will not be able to make any new signings over the next two transfer windows and will be without Eden Hazard and that is why he wanted to make sure that he would be given time, something that is not normally the case at Chelsea.
The former England midfielder is concerned that he could damage his reputation at Chelsea at a time that he is just starting his managerial career but it seems that Abramovich has said enough to assuage those concerns.
Lampard will be joined at Stamford Bridge by Jody Morris and Shay Given who have both been working with him at Derby but one former player that will not be in the dugout is John Terry, who is said to have fallen out of favour with the Russian owner.
It is just a matter of time now before an official announcement is made confirming Frank Lampard as the new Chelsea manager.