Gunners manager Arsene Wenger had Bailey scouted during Bayer's recent games against Hannover 96 and Borussia Monchengladbach, and the club's scouts were impressed by his performances, according to Steve Bates at the Sunday People (h/t the Mirror).
The 20-year-old scored a brace in the 4-4 draw with Hannover before hitting the winner in the DFB-Pokal quarter-final win over Gladbach.
Bayer Leverkusen showed exactly what Bailey can bring to a team:
Scouted Football also demonstrated just how effective he has been this season:
Bayer Leverkusen sporting director Rudi Voller has said the club would have to consider offers for "crazy sums," per Stephan Uersfeld at ESPN FC.
Bailey joined Leverkusen on a five-year deal in January. He has scored six goals and provided four assists in 14 Bundesliga outings this season.
Arsenal, meanwhile, may be in need of attacking reinforcements, having already lost Alex Oxlade-Chamberlain and with Alexis Sanchez and Mesut Ozil's futures still uncertain.
Bailey has shown himself to be an exciting option this season, but luring him to the Premier League midway through the campaign will be difficult and potentially expensive.
Meanwhile, Giroud's agent, Michael Manuello, will be in London for discussions over the striker's future, with the Frenchman concerned his lack of playing time may adversely affect his FIFA World Cup 2018 hopes, per the Sunday Mirror's Tom Hopkinson.
The 31-year-old has scored seven goals for Arsenal in all competitions this season, but he has started just once in the Premier League.
WhoScored.com showed just how effective Giroud has been coming off the bench for Arsenal:
That would surely ruin any potential move away in January, and his future may well depend on the severity of his injury.