Fellaini signed a five-year contract when he arrived from Standard Liege in 2008 but has recently been linked with Chelsea, Manchester United and several clubs in the major European leagues.
The 23-year-old midfielder was expected to be out of action for the rest of the season after surgery on his ankle last month but he could be back to help Everton's push for a Europa League place.
Point to prove: Midfielder Fellaini (centre) is happy to stay with the Toffees
'Everton really care about me,' said Fellaini. 'My relationship with the manager is excellent and I'm delighted that he considers me a key player and wants to extend my contract.
'The discussions have not yet begun, but I don't suppose they are far off. For my part, I'm ready and waiting.
Good news: Everton manager Moyes
'I've not been in contact with any other club about leaving Everton. Besides, they will have their say if a club show formal interest in me. 'I'm still under contract with them and I'm counting on returning to training as soon as possible and being available for the end of the season.
'My operation went well. The plaster came off on Monday and that will allow me to fully begin my rehab.
'If everything goes well, I hope to be able to help Everton at the end of the Premier League season.
'I'm happy with our recent results. We've not lost in the league since February 13 and a Europa League place is possible for us.'
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