The former Sweden centre-back says Forster is good enough to play for the Three Lions even though he is in the Scottish Premier League but feels his performances in the Champions League will go a long way to edging out current England number one Joe Hart.
"Fraser can challenge to be England goalkeeper by playing in Scotland but it is going to be important for him to play a lot in Europe," said Mjallby. "The game in Scotland is in a bit of disarray right now.
"It is hard for us. But we have shown, by bringing players from all over the world and without spending much, it is possible for us to build quite an interesting team.
"I am well aware Joe Hart is a magnificent goalkeeper but there is no reason why Fraser can't compete with him.
"His improvement during the two years he has spent with us has been fantastic.
"When he first came to us we were a bit surprised he was third choice for Newcastle.
"He was very solid during that loan year, and really important in helping us win the title.
"He spends a lot of time on the training ground, and his concentration is very good. He is a very trusted soldier for us.