The problem has kept the former Bristol City and Cardiff stopper out of action since September but he is confident of his chances of overhauling club teammate Nick Pope before Gareth Southgate names his squad for the tournament.
"I am back into full training on the grass as of last week and I have played a couple of reserve team games," Heaton explained at the launch of his new Precision Infinite Heat glove range.
"In the next week or so I am expecting to be back to 100 per cent and hopefully get back in the team.
"Being back fit is the first marker and then trying to get back into the team is the next step. Beyond that I still have ambitions of making the plane for the World Cup and there is a fair bit of water to go under the bridge yet.
"I am working every day with that ambition in mind."
Heaton faces stiff competition for a place in the squad, with Pope, Joe Hart, Jordan Pickford and Jack Butland among the players battling to be in Southgate's plans.