The England Under-21 star yesterday confirmed he will stay at the Blues — having helped fire Aston Villa to the Prem while on loan.
He said: “He is a great manager and it would be great if it was him who took over.
“I believe in myself and there is no better guy to play under: Someone you have grown up watching, been at Chelsea for ever. He knows about me as well."
Abraham played against Lampard's Derby when Villa beat them 2-1 in the Championship play-off final last month.
The frontman added: “I didn't really get the chance to speak with him afterwards. I was on the pitch for hours celebrating.