Steve Bruce's Tigers are currently four places higher than the defending champions, in eighth, having won three and drawn one of their opening six fixtures.
United suffered their third defeat of the campaign on Saturday, losing 2-1 to West Bromwich Albion, as their faltering start under the leadership of David Moyes continued.
However, despite Hull being three points better off than United, Davies has called on his side to remain focused on the job in hand - securing Premier League status.
"If we end up above United, I will streak around the KC," he told the Daily Express. "I'm not too sure it will happen but it's just good that we are doing well.
"With United down there, it's a big shock for the league.
"Ultimately, we are just doing all we can to push as high up the table as we can and, hopefully, be safe as quick as possible."
Hull are unbeaten at home and host Aston Villa on Saturday, with centre-back Davies relishing the prospect of facing his former club, who themselves have endured a turbulent start to the 2013/14 season.
"It's a bizarre one because Villa this season have been up and down," he added. "They have beaten Arsneal away and Manchester City and then probably lost a couple they shouldn't have.
"You don't know what you are going to get.
"We need to go into the match with the confidence we have taken from the last couple of wins and, hopefully, make it three and push further up the table."