Bordeaux coach Elie Baup is ready to sacrifice the defensive midfielder, in order to bring in Jerome Leroy from Marseille on a four-year contract.
Legwinski is believed to be keen to leave and the Girondins club have received contact, although no firm offers, from Borussia Dortmund and The Hammers.
The Londoners' bid is more lucrative, although the lack of European football at Upton Park next term may count against them.
Roeder has already taken a number of French players on trial since replacing Harry Redknapp.
Meanwhile, Sunderland are being urged to meet Francois Grenet's asking price after his proposed move to Middlesbrough fell through when Steve McClaren failed to meet the asking price.
With the injured Christophe Dugarry and Herve Bugnet, who was involved in the Under-20 World Cup, missing at the start of the season, Bordeaux could move in the market for a new striker with a number of names in the frame.
Guingamp's Fabrice Fiorese, Rennes hit-man Cyril Chapuis and Toulouse duo Fabrice Jau and Victor Bonilla have all been mentioned.
