The 33-year-old is confident that the club’s trophy drought is set to end.
“I’d love to finish my career here,” Given told the club’s official website. “I haven’t been here long, but I already feel at home and love the club.
“I grew up a Celtic supporter and they have a big place in my heart, but I really hope I can finish my career here. You can never say never, but I’d like to think I will.”
He added: “We’d like to win something. If it doesn’t happen this season, it’ll happen next. But hopefully we’ll be able to do it (this campaign). We’re in the Carling Cup quarter-finals, we’ve got the FA Cup to come and we’re up near the top of the league.
“If we win our game in hand we’ll only be a couple of points behind United. We need to keep going and winning away games, which will be crucial.
“We have a fantastic team and a strong squad, but it will be tough because there are some great sides in this league.
“Manchester United and Chelsea will be the teams to beat. They also have experience of challenging for the title – they’ve both been there and done it. But we believe in ourselves. It’s a long winter and a long, hard season – there’ll be a lot of twists and turns between now and the end of the season.”