Burke and Zohore have both struggled to nail down a solid role at Albion since joining the club, with Burke spending this season on-loan at Alaves in La Liga.
The Scot signed for the Baggies in 2017 in a deal worth approximately £15m, whilst Zohore joined the club for approximately £8m last summer from Cardiff - making 17 Championship appearances, he featured just twice in Albion's final 16 games.
The Danish striker completed 90 minutes in the league just once in Albion colours, during their 1-1 draw with Derby in August.
Gibbs meanwhile has been a key component for the Baggies since joining the club from Arsenal in 2017, but has struggled with injury in recent campaigns.
The 30-year-old totalled just 15 appearances across all competitions this season for the Baggies, having been hampered by frequent muscular injuries.
Reports suggest that due to the club's promotion, Gibbs' wages will be set to increase - meaning he's likely to be made available to willing buyers, with Antonee Robinson reportedly being targeted as a potential replacement.
The reports also claim that youngsters Sam Field and Jonathan Leko could also be made available for potential deals, with both spending last season on-loan at Charlton.
The pair have both been on the books at Albion having risen through the youth ranks at The Hawthorns. Both suffered various injury struggles at The Valley, with Leko suffering a season-ending knee injury in December.