Arsenal could propose a new contract to centre-back Laurent Koscielny, who they are not at present ready to let leave.
Lyon have prepared a two-year contract for Koscielny, but will need to reach an agreement with Arsenal for the move to go through.
Borussia Dortmund and Rennes have also been linked with the 33-year-old, whose current Arsenal deal is due to run out in around 12 months.
But, according to French sports daily L'Equipe, Arsenal are not yet ready to let Koscielny go.
The Gunners could, it is claimed, even offer Koscielny a new contract to keep him at the Emirates Stadium.
Apart from Koscielny, Lyon are closely watching two other defenders in the form of Manchester United's Eric Bailly and Sampdoria's Joachim Andersen.
Les Gones had been expected to recruit one centre-back this summer, but they could bring in two.
Koscielny is believed to be ready to return to France if Arsenal choose to let him leave.
