Hull City reject Maguire bid
The former Sheffield United defender made just two starts last season in the Premier League and spent the final three months on loan at Wigan Athletic.
However, Bristol City - League One champions in 2014-15 - want Maguire to spearhead their defence in the second tier.
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Hide AdCity, though, rebuffed a bid that would have allowed the Yorkshire club to recoup the £2.5m spent on the defender a year ago.
It is not clear yet whether the Robins will make a second offer but Steve Bruce is not keen to sell, instead expecting Maguire to challenge for a first team place in the coming season.
Paul McShane, who left Hull late last month, has joined Reading.