Frei, 22, has fallen out of favour at Besiktas this season and is going for a transfer in January. The Baggies consider the former Fulham winger to be a perfect player for their squad, with Tony Pulis keen to add more attacking width to his side.
However, Frei is only a back-up option ahead of the transfer window, with Pulis preferring to sign Matt Phillips of QPR.
Phillips was a summer transfer target for the Baggies, and the report claims that they are ready to revive their £7 million bid for the winger. Phillips impressed in the Premier League last season, and the 24-year-old has continued his good form this term, with four goals and two assists in the Championship.
The Baggies were ready to swoop for him, but the report claims that the appointment of Jimmy Floyd Hasselbaink has made that task harder, with Pulis believing that the new head coach will want to keep ahold of the winger to get back to the Premier League.
Should a move for Phillips collapse, Pulis will sanction a swoop for Frei, but only on a loan deal. Besiktas have offered Frei to Premier League clubs, and West Brom look a likely destination for when the transfer window opens next month.
The report states that both Newcastle and Norwich are also interested in the winger.