Bangura spent the second half of last season on loan to AIK who sold him to Celtic for £2m in 2011.
AIK felt that they were in pole position to get Bangura for a third time but failed to match the loan fee offered by Elfsborg.
A statement on the AIK website read: “AIK have been in talks with Celtic since Mohamed returned to Scotland but it emerged that Celtic wanted a higher fee than we paid in the autumn.
“Another Swedish club has agreed to meet that price and we won’t change our view on loan players.”
AIK sports director Jens T Anderson added: “This would require more money than we have spent previously on any loan player.”
The opening game of the Swedish season is between AIK and Elfsborg on April 1 with Bangura’s loan being for the entire season.
FIFA rules don’t allow players to be with more than two clubs in the same season but since it’s a new Swedish season starting in April Bangura is able to join Elfsborg.
Last week he scored his first Celtic goal in the 2-1 friendly win over Steaua Bucharest in Marbella.
Despite that goal his chances at Celtic would be limited with half a dozen strikers ahead of him in the queue for a place in Neil Lennon’s starting XI.
Since the start of the season Lennon has brought in Miku and Lassad Nouioui as well as giving Tony Watt a new contract.
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