Rangers have secured the signing of midfielder Nicky Law from Motherwell.
Cardiff boss Malky Mackay insists midfielder Peter Whittingham is part of his plans for next season.
Bangura recently returned from a loan spell at former club AIK last month but failed to force his way into the starting line-up, despite scoring in a friendly against Steaua Bucharest this month.
The Sierra Leone forward has failed to score in 13 competitive appearances since joining Celtic for about £2million in August 2011.
The 23-year-old told Elfsborg's official website that he first heard of a possible transfer on Wednesday, but that both clubs had previously been in contact.