The 27-year-old, who has five caps for France, scored only one goal in 15 Ligue 1 appearances last season - a figure that he admits was below par.
The attacker would prefer to remain with the French giants if possible but says that he will "wait and see" with regards to the Baggies' interest.
"In 15 games last season I scored only one goal. That is not the kind of return I was expecting. There is some disappointment in that," Briand told reporters. "Lyon are a great club, though, and I want to continue here unless I am deemed surplus to requirements.
"I know West Brom have asked about me but nothing has been done as yet. Let's wait and see what happens."
Lyon has already sold one player to the Premier League this summer after Dejan Lovren's 10 million euros move to Southampton earlier in June.