Manager Jose Mourinho named a 21-strong group for the Group A clash in Istanbul on Thursday evening, with Mikhtaryan in with a chance of featuring for the first time since the Manchester derby in September.
Carrick's absence could be because of Ander Herrera's forthcoming domestic suspension, with the former England international tipped to replace him in midfield against Swansea on Sunday.
Anthony Martial and Tim Fosu-Mensah have been included after missing recent squads, while Jones is part of the travelling squad 10 months after his last competitive appearance.
The 24-year-old has recovered from a knee injury but fellow defender Smalling, who has been suffering with a foot complaint recently, has remained in Manchester, as have the injured Antonio Valencia and Eric Bailly.
United squad: De Gea, Romero, Johnstone, Blind, Jones, Darmian, Fosu-Mensah, Rojo, Shaw, Fellaini, Herrera, Mkhitaryan, Lingard, Mata, Pogba, Schneiderlin, Young, Ibrahimovic, Martial, Rashford, Rooney.