Jakkrit, 40, was attacked by two men on a motorcycle while driving his black Porsche near Ramkhamhaeng Soi 166 in Min Buri district on Saturday night.
The pillion passenger shot Jakkrit three times through the driver's window. Jakkrit succumbed to severe wounds and was pronounced dead at Seriruk Hospital in Min Buri. There was another passenger in the car who was slightly injured.
His wife, Nitiwadee Pucharoenyos, said on television on Sunday that her husband liked collecting Buddhist amulets, but she has no idea whether a conflict over the amulets was connected to his death.
Police are questioning Jakkrit's relatives and friends.
The officers need to "find a connection" between their accounts and the murder so they can rule out possible motives, said deputy city police chief Pol Maj Gen Thitirat Nonghanphitak, who attended a meeting on the murder yesterday.
Jakkrit competed in the 2012 London Olympics and was a former Southeast Asia champion and 2006 Asian Games bronze medal winner.
His mother and wife said Jakkrit had never told them about his problems or his conflicts with other people.
However, he had said if "something happened to him", he wanted his family to play a song Saeng Sut Thai (Last Light) by Bodyslam at his funeral, said his mother, Bunkhit Panichpatikum.
Earlier in the day, Jakkrit took his wife, who lives in a separate home, and their two children to have lunch together.
That night, he planned to have dinner at his wife's home.
"Phi Ex did plan to have dinner with us, but he was shot on the way," said his wife, referring to Jakkrit by his nickname
The couple has lived apart since July after Jakkrit was arrested for allegedly threatening his wife with a gun during a domestic argument.
Jakkrit, who was accused of attempted murder, assault and illegal possession of firearms, was later released on bail. After their marriage breakdown, Dr Nitiwadee said Jakkrit tried to mend their relationship.
He was renovating his house and planned to invite her and their four-year-old daughter and one-year-old son to live with him there.
"I planned to do that," Dr Nitiwadee said.
"Phi Ex met me every day, trying to patch up our woes. I was glad to see this change."
Mrs Bunkhit said that after the Saturday lunch, Jakkrit phoned her to share his feelings and sent her photos of himself and his family through the Line social networking application. "I told him I didn't know how to use the application," Mrs Bunkhit said.
"He laughed when I told him I just randomly pushed the phone buttons."
Pol Col Ek Ekasat, deputy chief of the Metropolitan Police Bureau's Division 3, pointed to drugs, sexual affairs, gambling and personal conflicts as possible motives behind the shooting.
Investigators did not rule out his marital problems but were not convinced that the July quarrel would have led to a revenge attack by his wife. Police are checking closed-circuit camera footage at the scene and searching for other clues to the shooter's identity, he added.