The rebel, known as Roman Ruiz, led the 18th division of the Farc, which operates in north-west Colombia.
The bombing was the latest in a series of attacks on the Farc by Colombian security forces.
The two sides are holding peace talks but have not agreed a ceasefire.
The Colombian air force said it bombed a rebel position near the town of Riosucio in north-western Choco province on Monday.
Sources in the security forces later told local media that among those killed in the raid was Alfredo Alarcon Machado, better known by his alias, Roman Ruiz.
However, Ruiz has been reported killed once before.
Last year, sources in the security forces announced he had been killed, only for the head of the police to deny it later.
Ruiz is believed to be the right-hand man of Pastor Alape, who is part of the Farc team negotiating with the Colombian government at peace talks in the Cuban capital, Havana.
About 40 Farc rebels have been killed since the security forces resumed their bombing raids.
President Juan Manuel Santos gave the order for the resumption after 11 soldiers were killed on 15 April in a Farc ambush in south-western Cauca province.
The attack on the soldiers caused outrage in Colombia, with many questioning the rebels' commitment to the peace talks.
The Farc had declared a unilateral ceasefire in December as a sign of its commitment to the talks.
It argued the ambush in Cauca had been a "defensive measure" taken by its rebels as they came under pressure from the security forces.
When the peace talks officially began in November 2012, President Juan Manuel Santos ruled out a ceasefire, arguing that the guerrilla had used them during previous negotiations to re-group and re-arm.
In March of this year, he did however order the suspension of bombing raids.
The peace talks have been going on for two and a half years during which the two sides have so far reached agreement on three topics on their five-point agenda.
An estimated 220,000 people have died in a half century of armed conflict in Colombia.
November 2012 - Formal peace talks begin in the Cuban capital Havana between the Colombian government and the Farc.
May 2013 - A deal is reached on land reform, one of the most contentious issues. It calls for fair access to land, and rural development, two key causes of the conflict.
November 2013 - The two sides agree on the political participation of the Farc should a peace deal be reached.
May 2014 - Both parties pledge to eliminate all illicit drug production in Colombia.
December 2014 - Farc declares a unilateral ceasefire.
March 2015 -  Both sides agree to work together to remove landmines. Colombia is one of the most heavily mined countries in the world.
April 2015 Government resumes air strikes after the Farc kills 11 soldiers in ambush.
May 2015 Farc suspends its unilateral ceasefire after government military operation kills 26 rebel fighters.
What is at stake in Colombia's peace process?
A commander of Colombia's largest rebel group, the Revolutionary Armed Forces of Colombia (Farc), was among five rebels killed in a bombing raid on Monday, the Colombian military says.