The former Manchester United assistant stepped into the role as caretaker following the resignation of Steve Bruce during pre-season before leading the Tigers to a shock 2-1 win over reigning champions Leicester City in their Premier League season opener on Saturday.
Regarding the interim role at the KCOM Stadium, captain Davies has implored the Humberside club to make the call and appoint Phelan as manager.
"Mike's made it clear he wants the job," Davies said.
"Most people would err on the side of caution, in case they don't get it.
"He wants to take on this mighty challenge, and we need someone like that.
"It's been difficult over the last few weeks in terms of knowing the next step, but as individuals, we've always believed in our own ability. It's just about knowing whether we get a few more players in to help us.
"I believe there is more to come from us, but it's going to be hard to do that week in, week out, because there's only so far you can get on emotion."
Hull will be looking to make it two wins on the trot when they meet Swansea City at the Liberty Stadium on Saturday.
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