The Russian owner has been a distant figure at Stamford Bridge in recent years after problems with the UK government over his visa.
Lampard tells The Athletic that Abramovich was “very visible at the training ground in the early years”, but that it was director Marina Granovskaia who he held talks with on his return as manager last year, not the owner.
“When I came back to the club, no; it was Marina (Granovskaia, the director), who contacted Derby and then myself to make that happen,” he said.
“I saw Roman on pre-season last year and it was big smiles and not cuddles but welcomes and handshakes.”
Lampard still reports back to Abramovich after games and insists he is honest in his feedback, even after a poor performance or result.
“From then, I haven’t had a close, close relationship with him, albeit I report back my thoughts on games, on where I see us and where I see us moving forward consistently through Marina and I’m very happy with that.
“I would say the relationship is close without being practically close day-to-day or week-to-week. I feel the support from afar, but it’s very straight, very cut-and-dried and that’s how I try to give it back.
“If I’m commenting on how we’re playing or performing, I don’t beat around the bush. Whether good or bad, I think that’s the right policy with a man of that level.”