The 19-year-old played six times for the club last campaign and was also sent out for a brief loan spell with Colchester United.
"I'm definitely looking for more," Potts told the Hammers' official website. "Every year, especially in pre-season, as a young lad you want to set your stall out for the rest of the season.
"You know pre-season games are going to give you chances and you have to take those chances to show the gaffer what you can do and if you're good enough to step up to the Premier League."
Potts signed his first professional deal with West Ham in 2011.