Davies made the tongue-in-cheek claim prior to last weekend's Premier League fixtures, which saw Hull beat West Ham and United slump to a shock defeat against West Brom at Old Trafford.
Hull heads into Saturday's home game against Davies' former club Aston Villa three points and four places ahead of United.
While Davies does not expect David Moyes' men to be lower than Hull come the end of the campaign in May, the 28-year-old is prepared to stand by his promise should Bruce's side achieve the feat.
"I said last week when I was being interviewed and someone asked, 'what's it like to be above Manchester United?' that I'd streak around the KC if we finish above them, but ultimately that's how ridiculous it is at the moment," said Davies. "I'm not sure I'd get away with it. I might get arrested on way round.
"It's one of those things that's a bit tongue in cheek, but if we actually did finish above them I guess I'd have to do it. We're six games into the season so being above Manchester United is nothing. We've got our own personal table to work towards and as long as we're top of that table that's all that matters."