Houghton, 50, was one of three candidates short-listed by the BCB in July after Dav Whatmore decided not to renew his contract.
The BCB's Gazi Ashraf Hossain said Houghton had informed the board he was not prepared to move from his home in England and had turned down the chance to interview for the job.
''He wants to stay with his father, who is about 85. So it is unlikely for us to get him now,'' said Ashraf.
The other two candidates on the short list are Australians John Harmer and Jamie Siddons. Harmer attended an interview on Aug. 31.
Australia's Shaun Williams has been in charge of the Bangladesh team since Whatmore's exit and will be coaching the side through this month's Twenty20 World Cup in South Africa.
Fixture: Twenty20 World Championship