Köhler had met Klar, who turns 55 later this month, in a southern German prison on Friday, a spokesman said, confirming a report published in the news magazine Der Spiegel. Köhler is to announce his decision on the clemency application during the course of the week.
Klar, who was sentenced to life in prison for the 1977 assassination of Chief Prosecutor Siegfried Buback and the abduction and murder the same year of employers' federation chief Hanns-Martin Schleyer, has been in jail for the past 24 years.
There is strong opposition in Germany to Klar's release, not least because he and other members of the "Rote Armee Fraktion" -- also known as the Baader-Meinhoff gang -- have refused to reveal details of the killings.
Klar called for "completing the defeat of the plans of capital and opening the door for a different future" in a letter read at a left-wing conference in January.
Conservatives against pardon