The US international, who can operate at left-back as well as in his more natural central defensive position, was a transfer target for the Baggies a couple of years ago before he joined the Trotters.
The 26-year-old actually spent a week training with Albion in December 2011 but joined Bolton instead a month later after also being offered the chance to try and earn a deal at the Reebok.
Baggies scouts have, however, kept an eye on him since and have watched Ream in action several times this season as he continues to impress in the Championship.
Reports claim the midlanders will once more have representatives at Tuesday's game against Doncaster and, if he shines again, a summer offer in the region of £4million could well be on the cards.
Bolton forked out £2.5million when signing him from New York Red Bulls and he has gone on to establish himself as an integral part of the Wanderers' side since, making 54 appearances.