Forster helped the defending champions win all five of their league fixtures last month without conceding a single goal.
The 25-year-old goalkeeper is aiming for a 12th consecutive clean sheet in Sunday's match with St Johnstone.
"I'm always very ambitious and don't tend to look back at all," said the England shot-stopper. "It's all about what you can go on and achieve and improve on."
Forster won his first England cap in November's 2-0 defeat to Chile and is hoping to make Roy Hodgson's squad for the World Cup in Brazil.
"I still speak to Dave Watson, the goalkeeper coach every so often," added Forster. "Everyone who is English wants to be on that plane to Brazil.
"To go and have that opportunity to be part of the World Cup in Brazil is a once in a lifetime opportunity."
England's most-capped goalkeeper Peter Shilton has recently said that Forster's international chances will be hindered as long as he stays in Scotland.
However, Forster disagrees, saying: "I've broken into the England squad through being at Celtic and I've gone on to win my first cap whilst playing at Celtic, so there's no reason why I can't go on to make the World Cup squad.
"All I can do is to try and play the best that I can and put in the performances week in and week out for Celtic."
Forster's award completes an awards double for Celtic, as Neil Lennon won the manager's award.