The Scot is out of contract at Hillsbrough, and with the Owls yet to appoint a new manager, Botlon boss Neil Lennon is keen to pounce to add some attacking threat at the Macron Stadium.
The News are saying that Wednesday have offered Maguire reduced terms, leading him to consider his future at the club.
Lennon would be somewhat familiar with Maguire with the player having spent the early years of his career at Aberdeen and Kilmarnock, while the Norther Irishman was still playing at Celtic.
Maguire has enjoyed a mixed few seasons in England, having been involved at a few clubs including Derby County, and loans spells at Portsmouth and Coventry City.
The 26-year-old has always managed to get a handful of goals at each club, but is yet to beat his season's best total of 12 from his final season at Aberdeen.
Would Maguire be a good signing for Bolton?
Capable of playing in a supporting role behind the striker or on the wings, the Scotland international would certainly bolster a side that for much of the second half of last season relied on 36-year-old Eidur Gudjohnsen and 37-year-old Emile Heskey to add depth to the striking department.
Loan signings Adam Le Fondre and Joe Mason are no longer at the club, so there is a genuine need to bring numbers in that can offer the Trotters something.
There is also a huge lack of options on the wings, with just Liam Feeney and Rob Hall available to Lennon of the present squad.
Maguire, who scored 8 goals in 42 Championship games for Wednesday last season primarily off the right wing, would certainly strengthen the wide areas of the side, and without Bolton having to pay a transfer fee too.