The Baggies are keen to add some extra firepower to their squad during pre-season and England U21 international Bamford could be an ideal signing.
The forward was excellent on loan at Middlesbrough last season, netting 19 goals in all competitions and propelling the club into the Championship play-offs, winning plenty of Premier League interest in the process.
However, Middlesbrough provided Bamford's third loan spell, having previously been loaned out to MK Dons and Derby County from Chelsea and he could now look to move on if his first team opportunities are limited at Stamford Bridge.
Jose Mourinho is known to be an admirer of Bamford's finishing quality, and Chelsea are believed to be keen to hold on to the 21-year-old as a back-up option for Diego Costa and Loic Remy, however that may not be enough.
Bamford has two years left to run on his Chelsea contract so the Blues could demand around £10m for their young striker, particularly as it would leave them short of first team strikers.
A move to the Hawthorns would see the striker link up with fellow England U21 teammate Saido Berahino - provided West Brom keep hold of him this summer - and former Everton forward Victor Anichebe.
Baggies manager Tony Pulis is also believed to be keen on Ligue 1 duo Andre-Pierre Gignac and Dimitar Berbatov.
Chelsea fans: Would it be wise for Mourinho to sell Patrick Bamford? Leave your thoughts in the comments section below!