The 33-year-old has found himself out-of-favour at Anfield after the summer arrivals of Christian Benteke, signed from Aston Villa for £32.5m, and £28.7m forward Roberto Firmino who joined from Hoffenheim.
Liverpool have been negotiated down from their initial £3.5m valuation of the England striker with the agreed fee being closer to £2.9m. Baggies boss Tony Pulis, speaking to the Daily Mail earlier this week, described the prospect of signing Lambert as 'like bringing a brand new car out of the garage'.
Pulis continued: "Rickie is available, Liverpool have made that known. We'd be interested as it's very important that we get players who will score goals. Rickie's got a great goalscoring record."
Spurs boss Mauricio Pochettino was also considering a move for the former Southampton man, who he managed at St Mary's, and hoped he could be a replacement for Villa-bound Emmanuel Adebayor.
However West Brom have stolen a march on the North London club while Leicester have turned their attention to securing at least two central midfielders to replace Esteban Cambiasso who rejected a new contract last week.
The Foxes remain interested in signing Internacional midfielder Charles Aránguiz despite the Chile international preferring to join Bayer Leverkusen. Claudio Ranieri, yet to make a signing at the King Power Stadium, is also hopeful of securing the services of Caen star N'Golo Kante and Inter Milan's Alessandro Cannataro.
Lambert is resigned to leaving Anfield this summer, despite being a boyhood Reds supporter, but would prefer to seal a switch which keeps his slim England prospects alive with the European Championships on the horizon.
While he still enjoys a positive relationship with Pochettino, a move to White Hart Lane may limit his opportunities to shine while Leicester currently have five first-team strikers including Andrej Kramaric, Jamie Vardy and Shinji Okazaki.
This appears to make the Hawthorns his most likely destination but Norwich City also have shown an interest in the past. Pulis, on the other hand, has been buoyed by the £8m capture of Hull City defender James Chester yesterday afternoon.
On Lambert, he continued: "From what I can gather from people at Liverpool his fitness levels are very very good, and he is desperate to play football."