The 25-year-old was handed the chance to play Championship football by the Baggies in August 2022, joining from League Two outfit Salford City.
Thomas-Asante as finished as West Brom's leading goalscorer in back-to-back second-tier terms, scoring seven and 11 goals respectively in each Championship campaign.
Impressive performances in club football have led to international recognition for the attacker, who featured for Ghana during their World Cup qualifiers in June.
Since swapping the Peninsula Stadium for The Hawthorns nearly two years ago, Thomas-Asante has made 78 competitive appearances for the Albion, scoring on 21 occasions.
Southampton 'planning' swoop for West Brom's Thomas-Asante
According to Football Insider, Thomas-Asante's commendable displays over the past two years in the Black Country could be set to earn him a lucrative move.
The report claims that Premier League newcomers Southampton are plotting a deal to secure the services of the 25-year-old ahead of the new campaign.
It is understood that the Saints are in the market for a new striker this summer following the departure of Che Adams to Serie A outfit Torino.
Adam Armstrong, who recently signed a three-year deal at St Mary's, is the main source of goals for Russell Martin's side, with Thomas-Asante set to play a backup role should he move to the South coast.
Southampton struggled to pose an attacking threat during their top-flight relegation campaign of 2022-23, netting just 36 times in 38 Premier League matches as their decade-long spell in the division came to a sobering end.
What could Thomas-Asante offer Southampton?
Following modest goalscoring returns for Salford in the fourth tier, some West Brom supporters were underwhelmed by the addition of Thomas-Asante during the summer window of 2022.
However, the Ghana international has since established himself as a fans' favourite at The Hawthorns, as well as a key member of Carlos Corberan's starting XI.
The injury struggles of Daryl Dike and Josh Maja have resulted in plenty of game time for Thomas-Asante, who is now attracting interest from further up the football pyramid.
For what the 25-year-old lacks in pure ability, he makes up with unrelenting energy and enthusiasm - qualities that could be useful for the newly-promoted Saints.