The 22-year-old Swede arrived at Parkhead last 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.
The SFA and SPFL are 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 if he is to play for the Hoops in the Europa League group stages.
A joint statement issued on behalf of the two Hampden-based governing bodies read: "With regard to transfer window activity being undertaken by Scottish clubs on Monday, 1 September, the SPFL had an 11pm transfer deadline in place for registrations while the Scottish FA had a midnight deadline.
"At 10.56pm last evening, the SPFL received a request from Celtic FC to extend the SPFL deadline for registration of John Guidetti to fall in line with the Scottish FA midnight deadline. The SPFL agreed to this request.
"Celtic FC began uploading the relevant documentation in respect of the player prior to the midnight deadline.
"Where an International Transfer Certificate (ITC) is required for a player, it is custom and practice for the player's registration to be conditional upon subsequent receipt of an ITC.
"Due to part of the registration documentation being received by the Scottish FA very shortly after midnight, FIFA have not allowed registration by the Scottish FA of the transfer.
"The SPFL and Scottish FA are writing to FIFA in support of Celtic FC's petition that FIFA permit the Scottish FA to register the player with the Scottish FA."