Drugs lords, some in cahoots with ultra right-wing paramilitary squads, have long had links with the sport in Colombia.
"We'll put a brake on any kind of macabre association between delinquents and sports clubs," Santos said in a speech at a ceremony giving baseball player Edgar Renteria the award as Colombia's Sportsperson of the Year.
"Either we change football or football will end for us," he warned.
Santos said his government wanted "to eliminate any chance of bad apples being entrenched in this sport" adding that football 's links with drugs and paramilitary groups was repugnant.
A major brewery recently withdrew its sponsorship of the Bogota-based team Independiente Santa Fe during an investigation into the alleged laundering in the club of millions of dollars of drugs money.
Santa Fe are top of their group in the Clausura championship title play-offs.
The Colombian Football Federation was recently at the centre of a scandal when its financial advisor Manuel Bernal Vargas, shot by gunmen in Bogota in July, turned out to be the accountant of Salvatore Mancuso, a paramilitary leader extradited to the United States and accused of dealing in drugs.
America, one of Colombia's biggest clubs, has been owned since the 1980s by brothers Miguel and Gilberto Rodriguez Orejuela, heads of the Cali drugs cartel who are in prison in the U.S.
The club is on the so-called Clinton list of organisations people and companies are banned from doing business with at risk of severe sanctions.
