Belgian newspaper Het Nieuwsblad had earlier on Sunday published quotes attributed to the Toffees star in which he appeared to confirm he would be looking to leave the club, possibly as early as January.
But in a statement published on his Facebook page, Fellaini expressed his surprise at the speculation surrounding his future, insisting he remains fully committed to the new season with Everton.
|15/2||Everton are 15/2 with William Hill to beat Newcastle 2-1 next Monday
"I was very surpised to read in some newspapers that I will leave Everton very soon and perhaps next January," he wrote.
"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 realize a good championship in the line of the end of the last one.
"So with Everton, I am ready to play all the season and to reach our goals of this season. 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 has attracted much praise for his start to the new season, and is believed to be the subject of interest from a number of top clubs in England and elsewhere in Europe.