Six people died when the twin-engine plane came down in the Engativa neighbourhood.
It was travelling to the nearby town of Guaymaral to pick up former president Andres Pastrana.
Forensic experts said they did not find any traces of explosives on the bodies of the plane’s passengers.
The Beechcraft plane came down just minutes after taking off from Bogota’s El Dorado airport.
It was heading to Guaymaral, where it was due to collect Mr Pastrana and former defence minister Marta Lucia Ramirez to take them to a campaign rally.
But Mr Pastrana, who governed Colombia from 1998 to 2002, said he had cancelled his plans a few hours earlier.
“We were going to go on that plane, the flight plan from 10:00 had us down to board it. I was on stand-by until 14:00 when I finally decided not to go on it,” he told Efe news agency.
The plane crashed just around 16:20 (21:20GMT).
He also asked the Colombian defence minister to investigate if the crash could have been an attempted attack on his life.
Mr Pastrana recently resigned from a commission created by Mr Santos to advise the president on peace negotiations currently under way with Colombia’s largest rebel group, Farc.
He said he had serious doubts about a deal the government reached with the left-wing rebels on transitional justice.
The former president has been a target of attacks before.
In 1988, he was kidnapped and held for a week by the Medellin drugs cartel who wanted to pressure the then-senator into opposing the extradition of cartel leader Pablo Escobar to the US.
Mobile phone footage shows the plane coming down almost vertically into an area of two- and three-storey homes south-east of El Dorado airport.
Witnesses said they heard loud explosions after it hit the ground.
A corner bakery went up in flames, with an employee and the bakery’s former owner among the six people killed.
The remaining four victims were the pilot and three passengers who have yet to be identified.
Relatives of the pilot said he had decades of flying experience.