Tehzeeb Karim, 33, went missing from the Shahjalal International Airport on May 17, his family members said.
Tehzeeb's brother Rajib Karim, a follower of Anwar al-Awlaki, a militant known to be associated with al Qaeda, is serving a 30-year term in a UK jail for plotting to blow up a plane in 2011, the bdnews reported.
His father, Zainul Karim, was quoted as saying that Tehzeeb returned from Bangkok after an English language course but went missing from the airport on May 17.
After the reports that the Rapid Action Battalion's list featured Tehzeeb's name, his father called for the release of full details about such missing individuals.
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He expressed his suspicion that his son could be in the custody of a Bangladeshi law enforcement agency.
Zainul said Tehzeeb had been questioned by officials at the British High Commission in Dhaka when they went there after Rajib's arrest.
He said Tehzeeb married Seerah Rashid, his classmate in Scholastica school, after completing his A-Levels.
Zainul said his son Tehzeeb had been in Pakistan but did not tell his father. He had later gone to Yemen, saying he had managed a job as teacher there.
Zainul, who had been involved with Chhatra Union, an organisation of Leftist students, had contested in the 191 national election with a BNP ticket from Sunamganj, but failed to get elected.
Tehzeeb's eldest brother, Atif Karim, had died in a 'mysterious' accident in London in 2001, the family said.