Blackburn were looking towards signing the Nigerian defender on the January transfer window deadline day but failed to secure the proper paperwork to finalise the deal.
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On Tuesday, January 31, transfer deadline day, Blackburn made moves to sign the Nigerian international but were frustrated as the document for the transfer could not be assessed by the Football and Scottish .
Blackburn and Celtic are now waiting for the paperwork to be assessed at the Football and Scottish League offices in Preston and Glasgow respectively to check that all is in order with a final decision expected later on Wednesday.
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Ambrose joined Celtic in 2012 and has won four Scottish league titles, making over 150 appearances.
If the move is not confirmed by Wednesday, the defender will return to Celtic.