The France international struggled for game time in 2012/13, sparking summer transfer rumours.
West Brom have sounded out the possibility of taking the 27-year-old to England, as they attempt to bring creativity into their attacking ranks.
Briand is ruling nothing out, but is adamant that he has expressed no desire to leave Stade Gerland.
He is now waiting to find out what Lyon have planned for him, with the Ligue 1 club having admitted that they may have to sanction sales in order to generate transfer funds.
Briand said on his future: "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.
"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."