File photo of Manchester United chief executive Richard Arnold (Photo: the club s official website)
But he promised new manager Erik Ten Hag, who will replace interim boss Ralf Ragnick, would have money to spend in a video clip posted on social media.
Fans had been planning a protest outside Arnold's home amid ongoing unrest about the ownership of United by the US-based Glazer family.
Arnold, who heard about the protest plan, then met with the supporters at a nearby pub instead.
The chief executive, who replaced Ed Woodward earlier this year, bought drinks for the group and discussed a range of topics, including the owners, financial issues, and United's pursuit of Barcelona midfielder Frenkie De Jong.
This meeting followed United's worst Premier League season in terms of points, the club finishing sixth with a tally of 58 following only 16 wins from their 38 games. They also failed to lift a trophy in a campaign where Ragnick took over from the sacked Ole Gunnar Solskjaer, a former United striker, in November.
Arnold, seemingly unaware he was being filmed, said of United's financial position: "We spent a billion pounds on players, we spent more than anyone in Europe. I'm not thrilled where we are.
"What's happened is we've burnt through cash. I don't think we've done well with the money we've spent historically.
"For this summer, the money that the manager and the director of football want is there."
He added: "For the future, for investing in a new stadium and that sort of stuff, to do a latest and greatest £250 million ($306 million, 292 million euros) training ground, we've got to do something, we've got to get investors in.
"I need that to do what I want for the club. I've got to have more cash than we have now because no club in the world has the money to do a new stadium without getting it from somewhere, no one generates that - you either borrow it or someone invests it."
A spokesperson for Manchester United said: "Richard heard that a group of fans had gathered in a pub near his house.
"He went to meet them, bought them all a drink, listened to their views, and explained what the club is doing to deliver success on the pitch, improve the stadium, and strengthen engagement with fans."
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