A pair of South Korean Christian missionaries and their 12-month-old daughter are among those on the missing AirAsia jet that lost contact with air traffic control on Sunday, it has emerged.

Park Seong Beom, his wife Lee Kyung Hwa and daughter Park Yu Na were flying to Singapore to renew their visas, according to the Wall Street Journal. They were missionaries in Indonesia from Yeosu, a fishing village just over 280 miles south of Seoul.

A senior figure at the Yeosu First Presbyterian Church, which Park had attended since childhood, described him as "a very devout Christian".

"After working four years in Cambodia as a missionary, he [Park] had been sent to Indonesia, where he worked hard doing his missionary work and teaching Korean and computer to kids there," Choi Hong Koo said.

"I still can't believe the family is missing."

Also among the 162 people travelling on flight QZ8501 were British businessman Choi Chi Man and his two-year-old daughter, who had planned to leave Indonesia on an earlier flight but were unable to secure seats. Choi's wife and son left on the earlier plane.

The Airbus A320-200 disappeared over the Java Sea just five minutes after its pilot failed to get permission to fly higher to avoid bad weather on Sunday. The plane did not issue a distress signal.

The head of Indonesia's search and rescue agency, Bambang Soelistyo, told reporters on Monday that the plane is thought to have crashed and is now likely to be "on the sea floor".

"Based on our coordinates, we expect it is in the sea, so for now (we think) it is on the sea floor," he said during a news conference in Jakarta.

Relatives are gathering at Surabaya's Juanda International Airport as they wait for news.