Lyon are closing in on the signing of Memphis after agreeing terms with the player but discussions are still ongoing between the two clubs regarding the fee.
Memphis is believed to be interested in a move to France as he looks to revive his stalling career.
Lyon lodged an opening bid of £13 million last week which was rejected but an improved offer could see the French side capture their main transfer target as early as this week.
Memphis has failed to impress at United since his arrival from PSV Eindhoven in May 2015 and he now finds himself way down in the pecking order at Old Trafford, with the likes of Anthony Martial, Henrikh Mkhitaryan and Jesse Lingard enjoying greater playing time on the flanks.
The 22-year-old has appeared just eight times for the Reds this season, with his last appearance coming in November against Feyenoord in the Europa League.
He is yet to start a single game in the Premier League this campaign, with a total of 20 minutes playing time so far in the top flight in 2016/17.
Many have viewed the Dutchman's time at United as a massive underachievement following his time with PSV.
In the 2014/15 season, Memphis netted 28 goals in 40 appearances for the Dutch side as they captured their first Eredivisie title since 2008.
However, during his time in Manchester, the youngster has scored only seven goals in 52 appearances over the last two seasons.
Reds boss Jose Mourinho is prepared to let Memphis leave in the January transfer window as he looks to boost his transfer funds to launch a world record £100 million bid for Atletico Madrid forward Antoine Griezmann in the summer.
Mourinho has already offloaded midfielder Morgan Schneiderlin this month to Everton.