FARC has been battling successive governments in Bogota since 1964. Officials say more than 600,000 people have died and several million citizens have been displaced. FARC guerrilla numbers are said to be down by half from a peak of about 16,000 in 2001 but the group still poses a major threat, officials say.
FARC and the Santos government are deadlocked on the rebels' demands for sweeping amnesty, ambiguity about the numbers of citizens taken hostage over the years and rebel leaders' future in Colombian politics.
Uruguay's El Pais newspaper said Mujica was approached by Santos to help break the stalemate in talks taking place in Havana, Cuba. Santos wants Mujica to be "much closer" to the negotiations than he has been as a non-Colombian political figure of considerable standing in Latin America's left-wing movements.
Mujica was a Tupamaros urban guerrilla activist in the 1960s and 1970s. He was frequently imprisoned and was shot by police six times but survived. Leading a Broad Front coalition of left-wing parties, Mujica won the 2009 presidential election and took office in March 2010.
Colombian Foreign Minister Maria Angela Holguin made the approach to Mujica when she visited Montevideo.
"We want Mujica to visit Colombia, we want him closer to the peace process in which we are involved in Colombia," Holguin said. There was no immediate comment from the president.
She said Bogota was "extremely grateful" to Mujica for his support to the peace process. He issued an international appeal for hastening the Colombian peace process when he met with Pope Francis in Rome.
"President Mujica has much to say on this topic and we have much to learn about reconciliation, which is the stage to which Colombia is moving," Holguin said.
The reconciliation talks began in November 2012 but have snagged on how to bring former FARC guerrilla leaders into the political mainstream. Government negotiator Humberto de la Calle said talks would focus on establishing rules that could allow the transition of FARC to "an unarmed political force."
FARC argues Colombia's political system, currently dominated by two major parties, would make it hard for its amnestied leaders to get elected.
There are also other unsolved issues such as amnesty for former guerrillas who are wanted in the United States on terrorism-related charges.