The Daily Mail says the two giants sent scouts to watch the France Under-21 international against Motherwell on Saturday. Dembele converted a penalty to bag his seventh goal in three games for the Bhoys.
Dembele has become one of the hottest young prospects in Europe after a stunning debut season for Celtic in which he has scored 27 goals in 41 appearances.
Chelsea made an enquiry on deadline day in January over his availability, although the move never came about.
Dembele is keen to win a domestic treble with Celtic before considering his future.