The Hull Daily Mail says the Tigers have bid £1.5 million for the youngster.
But the Tigers are likely to see their first offer for the 21-year-old rejected, having seen Wolves fail with a bid of a similar amount.
Maguire has emerged as one of City's top transfer targets as they look to add more promising youngsters to their Premier League squad.
The centre-half recently indicated he wanted to stop holding talks about his future at Bramall Lane, and has again been told the ball lies in his court over his future.
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