The Hammers are currently one point adrift of safety in the standings with 14 games left to play.
Despite being involved in a scrap for survival, Cole is hopeful that West Ham can climb further up the table in the coming weeks.
"No-one seems to be safe from 12th downwards," he told the club's official website. "We're just focusing on trying to get to that tenth spot, that's our aim. If we can get there then we've had a successful season."
West Ham continue their Premier League campaign on Saturday when they make the trip to Aston Villa.