Bowkett was speaking after the briefing on the club's annual accounts, in which the board announced that all debts have been wiped after back-to-back seasons in the Premier League.
"We budget to finish 16th financially, so any money above that is a bonus," he told Norwich Evening News. "The continuous improvement objective for this football club is to improve from an 11th-placed finish in the Premier League, and that means we're looking for a top-10 finish.
"Financially with our forecasting, we budgeted last year to be 16th and then we did far better, which meant had more revenue and we could invest more in the club's 'software' – in the players, staff, Colney.
"So we've always sensibly budgeted for staying in the Premier League at a modest level, but the ambition of the football club – and Chris knows this – is continuous improvement."
Norwich finished 12th on their first season back in the top flight two years ago, before their 11th-place finish last year.