The 24-year-old was quoted as saying by Belgian newspaper Het Nieuwsblad earlier on Sunday that he "would look for another club or league" in January or next summer.
However, Fellaini has now said on his Facebook page that he is not seeking an exit from Goodison Park any time soon.
"I was very surprised to read in some newspapers that I will leave Everton very soon and perhaps next January," wrote the Belgium international.
"Let me remind you that I am very happy in Liverpool and our start of the championship was good.
"Kevin Mirallas and some other good players joined us to make a better squad in order to realise a good championship in the line of the end of the last one."
Fellaini added that he will play for Everton for the 2012-13 season.
"So with Everton, I am ready to play all the season and to reach our goals of this season," he wrote.
"However, my only concern for the moment is of course our (Belgium) Tuesday's game against Croatia.
"Whether you're in Belgium or England, thank you from my heart for your support..."
Fellaini joined Everton from Standard Liege in 2008.