According to reports in France, OL are on the hunt for a left-back with Ferland Mendy primed for a move to Real Madird.
One of the key men on their shortlist is Tierney, according to Soccer Link.
The Scottish international has been scouted by the club and their recruitment chief Florian Maurice.
It is believed that talks have taken place with Tierney's representatives.
Last summer Lyon, who finished third in Ligue 1, spent nearly £20million on Celtic striker Moussa Dembele and will play in the Champions League next season.
It was reported in the Catalan newspaper Mundo Deportivo that Tierney features on a shortlist for Barcelona, however the Spanish champions are not keen on matching Celtic's valuation of £26million.