The Sun is reporting that the Gunners have made a £50m enquiry about landing the 26-year-old England defender this summer but their interest looks set to be rejected.
According to the same story, Manchester United have already had a £70m offer for Maguire turned down by the Foxes this summer.
It is claimed in the same article that Manchester City have offered £65m plus £5m in add-ons, and that Leicester City will only consider doing business at around £85m.
Arsenal have now reportedly registered their interest in signing the England international, but they are said to be £35m short of the cash they need to be able to seal a deal.
It is also claimed in the same story that Arsenal have made a £40m offer for Wilfried Zaha, but Crystal Palace want closer to £120m for their star player.
Arsenal completed their first signing of the summer on Tuesday when they announced a deal to land Brazilian teenager Gabriel Martinelli from Ituano Futebol Clube.
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