The 22-year-old Swede arrived at Parkhead on Monday night for talks and it looked like he would be the final addition to Ronny Deila's squad which had been boosted the same evening by the signing of Serbian striker Stefan Scepovic on a four-year deal.
Guidetti's transfer was initiated but not completed before the deadline.
However, the Scottish FA is looking for FIFA to make "an exception" to allow Guidetti to move to the Scottish champions although he will have to be registered with UEFA before midnight tonight (Tuesday) if he is to play for the Hoops in the Europa League group stages.
A Scottish FA spokesman told Press Association Sport: "We will be contacting FIFA on Celtic's behalf to request an exception in order for the transfer to be concluded."
- Sports & Recreation
- Scottish FA
- Ronny Deila