Arsenal midfielder was substituted in the first half of Saturday's 3-0 win over Chelsea in north London.
Arsenal beat Chelsea 3-0 at the Emirates Stadium on Saturday in the Premier League.
Coquelin suffered a knee injury during Arsenal's win over Chelsea.
German was heavily linked with a move to Arsenal during the summer transfer window.
Theo Walcott has already scored three goals this season.
Arsenal take on FC Basel in their second Champions League group game.
Jenkinson has been out of actions since late January after suffering an anterior cruciate ligament injury.
Francis Coquelin suffered a knee injury during Arsenal's 3-0 win over Chelsea.
Mesut Ozil scored the second goal in Arsenal's demolition of Chelsea.
French coach admits he was "surprised" Costa left Atletico Madrid for Chelsea.
Theo Walcott made his 350th appearance for the Gunners against Chelsea.
Theo Walcott scored the second goal for the Gunners as Arsenal thump Chelsea.
The Blues suffered a 3-0 loss at the Emirates Stadium, only a week after going down at home to Liverpool.
Gunners beat the Blues 3-0 at the Emirates Stadium after goals from Sanchez, Walcott and Ozil.
Alexis Sanchez, Theo Walcott and Mesut Ozil were on the scoresheet for Arsenal against Chelsea.
Serge Gnabry rejected Arsenal contract extension to sign for Werder Bremen this summer.
Alexis Sanchez was not authorised to take the penalty against Hull City.
Arsenal have not won against Chelsea in five years in the league.
Wenger has won only once in his 15 appearances against Mourinho.
Mourinho had branded Wenger a 'speacialist in failure'.
Giroud came through an intense training session on Friday to prove fitness ahead of Chelsea clash.
Arsene Wenger will come up against Antonio Conte for the first time when Arsenal take on Chelsea.