The 29-year-old spent six months on loan at Hull City last season, however he could not save the Tigers from being relegated to the Championship.
He has since returned to Italy, where once again he is being overloked and struggling for game time. Tony Pulis is interested in rescuing the defender, as he looks to tighten up his defence ahead of the new season.
Premier League new boys Huddersfield have seen two approaches rejected, leaving West Brom as supposedly the best option if he is to move.
The Baggies do need a new defender to bolster their ranks at the back, with 37-year-old Gareth McAuley potentially in need of replacing.
But the Midlands side will have to act quickly, as Ranocchia, who keeps rejecting Genoa, could have to settle for another season in Italy.