The Hammers are currently above the relegation zone on goal difference following four defeats from their last five matches.
However, Bonds, who enjoyed a 25-year association with the club as a player and manager, believes that results will improve once the squad is fully fit.
"If you can get everybody back fit, I don't see them having a problem," he told West Ham's official website.
"It's easy for me to say from the outside because I don't have the job and I haven't got to worry about it now. I don't see them having any problem staying up, I really don't."
West Ham continue their Premier League campaign on Saturday when they welcome fellow strugglers Sunderland to Upton Park.