However, the Wales international midfielder claims the story was wide of the mark and that he is hoping to see out his football career at St. Andrews.
"I probably have left myself open by saying there is no other club I'd rather join than Everton," he told the Birmingham Evening Mail.
"But what hasn't been put in stories or on the television is the whole sentence.
"I said that would be the case 'if I ever leave Birmingham'.
"I love the club, we've got a great manager and I've played the best football of my career last season.
"Unfortunately, it's all come out that 'Robbie Savage wants to go to Everton'.
"I've never been happier here. Onething that gets me down is the travelling to and from Leicester so I'm actually looking at getting a house in Birmingham.
"That's a sign that, with the possibility of a new contract, it's perfect for me to stay.
"I think that if I have another good season like the last one, I will be around for a long, long time.
"Whether I will finish my career here, I don't know. It's a long time before it will end. But at this moment I cannot see myself going anywhere else."