Forster had a successful 2011–12 season with Celtic, winning the Scottish Premier League and helping his team beat the previous season's record of 23 clean sheets. He kept 25 clean sheets combined, Forster racking up 21 of them. Forster stated, "I'm very happy that I'm going to be at Celtic for the next four years at least", and added that "The manager's faith in me means a lot, I've loved my two seasons at Celtic and he's done so much for my confidence FIFA 18 Coins."

Forster's impressive performances for Celtic in the Champions League and involvement with the England international squad led to media reports in October and November 2013 that several clubs, including Manchester United and Manchester City, were considering to make a bid for the goalkeeper. Celtic manager Neil Lennon commented, "It's going to be impossible to keep Fraser, the way he's playing. Inevitably, I think a huge club will come in and make a huge bid for him."