The England international could be brought in at the Hawthorns to strengthen the frontline.
Tony Pulis has made reinforcing his forward line a priority this summer, and that has meant him casting his net far and wide when looking at possible additions.
The likes of Ba and Charlie Austin are just two of the players that they are said to have been looking at, according to the Birmingham Mail, but the Senegalese forward moved to China from Besiktas this month, while the QPR attacker is much in demand across the Premier League.
Former Southampton star Lambert had a desperately disappointing return to Liverpool last season, scoring just two goals, yet is another name the Baggies are keeping in mind according to the report, depending on whether Brendan Rodgers is open to him leaving this summer.
Would Lambert be a good signing for West Brom?
Looking at the 33-year-old's season at Liverpool, it is difficult to argue that Lambert would bring much to any Premier League side that he would move to, but the forward was afforded precious few chances to impress at the Reds, starting just one match in the first eleven league games.
Just a year before, Lambert had proved himself one of the best strikers in the division, so he hasn't become a poor forward overnight.
It is likely that the Baggies would have to be looking to find a place for him in the first team in order to try and drag the kind of form he exhibited at St Mary's back into his game, because he has already proved at Liverpool that he was unable to make an impact from the bench.
With Saido Berahino at the club, Lambert will have to be playing with the youngster or as his replacement, which may just see him restricted to the same opportunities he had at Anfield.