Guidetti travelled to Glasgow on Monday for talks as Celtic moved to complete their second striker signing of Deadline Day following the capture of Stefan Scepovic on a four-year deal.
The 22-year-old Swede’s move was initiated but was unable to be completed before Monday’s 11pm deadline.
A Scottish FA spokesman said: "We will be contacting FIFA on Celtic's behalf to request an "exception" in order for the transfer to be concluded."
Celtic would need to register Guidetti with UEFA before the end of Tuesday in order for him to be eligible for the Europa League group stages.
Guidetti, who joined City from Swedish side IF Brommapojkarna in 2008, spent the second half of last season on loan at Stoke where he mustered six appearances without scoring.
The youngster had a far more prolific spell with Eredivisie side Feyenoord three years ago when he notched 20 goals in 23 appearances.