The 25-year-old Belgium international has been made aware that the west London club have been tracking his progress at Goodison Park but insists he hasn't spoken to anyone at the club.
"If Chelsea want to sign me, then they need to come forward with a bid for me," he told The Sun.
"I have heard about Chelsea’s interest but I’ve honestly not spoken to them."
The Blues are not the only club in for Fellaini's services but the Belgian added that he is happy at Everton for the time being amid the interest.
|MOYES TRUSTING PIENAAR
|16/1||Everton are 16/1 with BetVictor to secure a 2-2 draw with Man Utd at Old Trafford
Everton travel to Manchester United on Sunday and could set themselves up for a top-four finish with a positive result, something Fellaini hopes he can achieve at Goodison Park.
"It might feel better to play Champions League football for Everton than Chelsea, as they gave me my debut in England," he added.
Fellaini is enjoying his most prolific season in England, scoring 11 goals in all competitions.