Having signed from Tranmere Rovers, Simonsen has steadily made progress in the Goodison Park reserves but is yet to secure the first-team jersey for himself.
Reports in the media have the keeper moving to Wigan as part of a deal for Roy Carroll, but Simonsen is keen to stake his place on Merseyside.
Speaking to the club's official website, Simonsen said: "I know I can definitely do a job in The Premiership.
"I have the utmost confidence in my own ability and it's just getting the opportunity to put together a run of games rather than the odd substitute appearance every few months.
"I am good enough to play in the Premier League. I have got no doubt about that. But if the gaffer wants to bring someone else in it is his decision.
"It is a little upsetting to pick up a paper and read that you may be leaving the club and the manager wants a new goalkeeper.
"But you just have to forget it really and get on with your job."
