United manager Jose Mourinho said on Friday the Premier League club had turned down an offer for the 22-year-old Netherlands international.
"I have put a priority on Memphis Depay," said Genesio.
"Things are progressing. We keep on working. It takes time because recruiting a player now is not easy."
Depay joined United from PSV Eindhoven for £31m in May 2015, signing a four-year contract.
He has scored seven goals in 53 appearances for the Red Devils but has not started Premier League game since Mourinho was appointed in the summer.
Speaking on Friday, Mourinho said: "The offer we had is far from being reasonable for us.
"He is our player. If nothing happens, he is one more for us."
Genesio described Depay as a "young player with great international experience and a lot of potential".
He added: "He has an interesting profile for us. But there are several things to consider, including the price."
Lyon, who visit Caen on Sunday (16:00 GMT) are fourth in Ligue 1, 10 points behind leaders Nice with a game in hand.
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Manchester United winger Memphis Depay is Lyon coach Bruno Genesio's "number one priority" during the January transfer window.