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The Netherlands international's links to Barca have been heavily aided by his relationship with Ronald Koeman, who coached Depay with the Dutch national team before taking over the La Liga giants this summer.
Having earned 59 international caps, Depay has scored 21 goals for the Netherlands, featuring for the third-place finishers at the 2014 World Cup in Russia.
Depay scored twice in Lyon's 3-2 win over Lens on Wednesday as they moved three points clear at the top.
While he is linked with a move, Depay said he may yet finish the campaign with Lyon rather than depart this month before his contract expired.
"I'm happy here. We have a great team, I really like the president, we'll see what happens," he told Canal+ following Wednesday's win.
"The president and I know what happened in the last four seasons. Let's keep going and enjoy my presence. I might be here until the end of the season.
"Let's focus on Saturday's game, let's be happy, we have a great team."
Only Paris Saint-Germain star Kylian Mbappe (16) has been directly involved in more Ligue 1 goals than Depay (14) this season.
But no player has created more chances than Depay's 42 for high-flying Lyon.
Depay has also created 10 big chances, with only Marseille forward Florian Thauvin (12) and PSG attacker Angel Di Maria (11) having created more.
The Dutch star originally moved to Lyon in 2017 after struggling to breakthrough with Manchester United.
Depay moved to Old Trafford in 2015, but scored just seven goals in 53 appearances during his time in England.