The Baggies and the Swans are both rebuilding their respective squads following their relegation from the Premier League last term.
Nmecha, who was born in Germany but has represented England at youth level, has enjoyed a promising pre-season, scoring his first senior goal in the friendly win over Bayern Munich.
According to the Daily Mail, Albion want the 19-year-old to play alongside Jay Rodriguez and Dwight Gayle if they can succeed in signing the latter on loan from Newcastle United, with Salomon Rondon going the other way.
The report claims that Swansea, who have just completed the signing of Man City winger Bersant Celina in a £3m deal, are also eyeing up Nmecha in their bid to immediately bounce back from the second tier.
Nmecha made his Premier League debut last season for the Citizens, coming off the bench for Gabriel Jesus against West Ham United at the London Stadium.