The goalkeeper was handed his England debut earlier this month and is confident his World Cup chances will not be affected by the club's exit from the Champions League
The 25-year-old has insisted he is happy at the Scottish champions amid speculation of a possible move away in order to boost his chances of making England's squad for the 2014 showpiece in Brazil following his debut earlier this month.
But Forster wants to remain at Celtic, at least for the remainder of the season, to repay the faith shown in him by the club, who were eliminated from the Champions League following a 3-0 defeat against AC Milan on Tuesday.
"Am I happy to stay here at least until the end of the season? Yes, Celtic’s a fantastic club and I don’t see that [being out of Europe] being a problem," Forster told the Daily Mail.
"This club has been fantastic for me over the past three-and-a-bit years. It's a huge club and I've loved every minute of being here since I first walked through the door.
"The gaffer Neil Lennon, [goalkeeping coach] Stephen Woods, [sports scientist] Bill Styles - they have all been fantastic for my career. They've brought my game on and developed me as a goalkeeper.
"It's obviously a big disappointment to go out of the Champions League but I'll take it a game at a time and not worry about the World Cup. It's seven months away and there is a lot of football to be played."