Matthews's current deal with Celtic runs out in June 2015 and the 20-year-old is happy to continue playing for the Glasgow giants beyond that term.
"The club has been great to me and I really enjoy being here so if I am offered a new deal I will happily sign, definitely," he told Sky Sports News.
"The club is massive. The Champions League is one of the main things, obviously, but the fans are brilliant and it is an honour to play in front of them every week so I am happy to stay.
"Every player wants to play in the Champions League but I think even without it Celtic are a massive club, so I am happy here."
Matthews joined Celtic from Cardiff City in 2011.