The Baggies will play the 2018-19 season in the Championship after they were relegated from the Premier League last season.
West Brom boss Darren Moore is looking to rebuild the squad and signing a good striker is one of his top priorities.
The report claims that West Brom are almost certain to lose striker Salomon Rondon, while there are doubts over the future of Jay Rodriguez as well.
In case the Baggies miss out on both of them, they will go for Roofe as a potential replacement.
The 25-year-old joined Leeds in 2016 from Oxford and has been a key player for the club since. Last season he scored 11 goals in the Championship in 27 starts, and registered three assists as well.
Roofe is a key player for Leeds and Marcelo Bielsa should do everything to keep hold of him. West Brom are also reportedly interested in signing Matej Vydra from Derby County.