Steve Bruce's side saw a bid for the Sheffield United defender rejected earlier this summer but he remains keen to get a deal done ahead of the 2014-15 season
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Bruce saw Maguire's talents first-hand last season as Hull overcame Sheffield United 5-3 in their memorable FA Cup semi-final clash.
And the former Manchester United centre-back has been suitably impressed by the one-time England Under-21 international.
Bruce told The Hull Daily Mail: "We like him. We tabled a bid which was rejected. I think we'll revisit it.
"We've watched him a lot over the last year and he's someone we've got an interest in. Let's see if we can get a deal done.
"There's a cap on how far we'll be prepared to go but that's the same for any player.
"I'm all for young British players and trying to give them a chance but with that comes a huge premium.
"In the old days you could get a League One player for £200,000. That's not the case anymore."