TMW says Liverpool, Bayern Munich, Juventus, AC Milan, Inter Milan and Tottenham are all in the running to sign the centre-back.
A fee of around £25m has been quoted as the asking price for Bremer, with Torino not settling for anything less.
It has also been claimed that Inter are the favourites to sign Bremer, with other players in that position said to be likely to leave.
The Brazil international penned new terms last year with Toro.
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