Arnold, 51, appears to be filmed saying United had “burned” through £1bn on players over the past few years.
He also says the money that new manager Erik ten Hag and director of football John Murtough want to spend on new players “is there”.
It is understood talks are continuing with Barcelona over Dutch midfielder Frenkie de Jong, who is Ten Hag’s number one summer transfer target.
United have not won the Premier League since 2013 and last won a trophy in 2017. They finished last season in sixth place, having sacked Ole Gunnar Solskjaer and replaced him with interim boss Ralf Rangnick.