Oxlade-Chamberlain is entering the last year of his contract at The Emirates Stadium.
The former Aston Villa player is not expected to be a part of Arsene Wenger's plans this season.
Asano scored four goals and provided four assists in 26 appearances last season.
Mbappe scored 26 goals to help Monaco win their first league title in 20 years.
Sanchez is attracting interest from Bayern Munich and Manchester City.
Perez has struggled for game time in the recently concluded season.
Chamberlain scored six and assisted 11 goals last season.
Martial endured a frustrating second season at Old Trafford.
Gunners will have tough task trying to entice world-class players due to lack of Champions League football.
Barkley has not signed fresh terms with his boyhood club, with his contract set to expire next summer.
Ozil and Sanchez both have their contracts expiring next season.
Lemar has scored 14 goals and assisted 14 for Monaco.
Sanchez, 28, only has a year left on his Gunners contract.
Bundesliga giants have paid around £36.5m to secure the services of the 22-year-old midfielder.
Lemar and Bakayoko played important roles in Monaco title winning campaign last season.
Talks between Ospina and Fenerbahce at an advanced stage, reports say.
Gunners boss Arsene Wenger also targeting Monaco duo Kylian Mbappe and Thomas Lemar.
England set to come up against both forwards in friendly against France.
Gunners have already signed Bosnian full-back Sead Kolasinac on a free transfer.
Sanchez has one year left on his current contract at The Emirates Stadium.
Long-serving centre-back and teammate Olivier Giroud have both been linked with returns to Ligue 1.
Golovin, 21, will be loaned back to CSKA by the Gunners for one season, according to reports.