Forster made his return from injury midway through January and the 27-year-old has kept clean sheets in all four Premier League appearances since his comeback.
His numerous saves against Arsenal on Tuesday saw Saints' manager Ronald Koeman label his performance as "magic" and hail him as one of the best keepers in Europe.
But while competition for the number one England spot heats up, Forster insists he is only focused on performing at club level.
"He [England manager Roy Hodgson] was always checking up on me and seeing how I was getting on, he was always there for me if I needed to speak to him," Forster said.
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Hart, Foster and Butland are all in contention to make the squad for the European Championship in France later this year.
"There are four of us now with Foster back from injury as well. Jack's obviously been around for a while playing with England Under-21s. He's a top keeper and that's what spurs you on to be better – having that competition," Forster said.
"It is one of them where I haven't even thought about it. Obviously the Euros is there but for me it is just a case of playing week in, week out for Southampton and then [we'll] see what happens.
"I've been out for so long and I'm just delighted to be back doing the thing I love."