The England international suffered the injury on the final day of last season and is yet to feature in Sam Allardyce's side's pre-season programme.
But he is hopeful of playing in West Ham's first-day clash with newly-promoted Cardiff City on August 17.
"I've been working hard," Carroll told the club's official website. "I've been away to Germany with the lads and keeping myself as fit as I can with the work I can do with my heel still being sore.
"It's been tough but I've been working hard to be back for the beginning of the season.
"Hopefully I'll be back for the start of the season."
Carroll completed a permanent move to Upton Park in June after scoring seven goals in 24 Premier League appearances in 2012-13 while on loan from Liverpool.