According to Salzburger Nachrichten, a deal between both clubs is nearing finalisation.
The 25-year-old midfielder remains under contract in Austria until 2029, but Salzburg could once again secure a significant transfer fee, with Bidstrup currently valued at around €13 million by Transfermarkt.
The club has already generated substantial income this summer following the sales of Joane Gadou, Kerim Alajbegovic and Jannik Schuster, totalling approximately €45 million.
Bidstrup has been a key figure under Thomas Letsch, starting 34 of his 36 appearances this season and contributing one assist.
If the move is completed, he is expected to strengthen Lyon’s midfield options and could arrive as a replacement for Tanner Tessmann, whose future is increasingly uncertain amid reported Premier League interest.