No one at the Federico Garcia Lorca Foundation was immediately available to comment, but the center said it would release a statement later in the day.
Last week, relatives of two other men believed to be buried in the same grave asked National Court judge Baltasar Garzon to order the grave opened. The request is part of a surging nationwide movement to give proper burial to the thousands of people known to have been killed by supporters of late dictator Gen. Francisco Franco and buried in mass graves.
But Lorca's family have long preferred to let the matter rest, leaving one of the 1936-39 war's most intriguing mysteries - the whereabouts of the poet's body - unresolved.
Investigations indicate the poet, who was open about his homosexuality, was shot along with a school teacher named Dioscoro Galindo Gonzalez and two labor union activists - Francisco Galadi and Juan Arcolla - on Aug. 18, 1936, near the Viznar mountain gorge in his native province of Granada in the south.
The four bodies are believed to lie in a site close to an olive tree and which has since been designated a memorial park to local victims. Others claim the burial spot is some 400 meters (yards) away.
Several thousand others are believed to have been shot and dumped at the gorge.
In a bid to build a reliable list of victims, Garzon asked church leaders, city mayors and other authorities this month for any information they have about victims of Franco's forces from the time of his military uprising in July 1936.
The rebellion triggered a civil war against the left-wing, democratically-elected Republican government, and was followed by a 36-year dictatorship.
Franco decreed that anyone who opposed him could face execution, and many of his victims were civilians. Lorca was among those who disappeared with no record of their fate or final whereabouts.
There is no official record of how many people died at the hands of Franco's forces during and after the war. British historian Paul Preston, an expert on Spain's Civil War, says 55,000 were killed by the Republican forces and were fully accounted for afterward.
Should Garzon find that there was a systematic campaign to kill Republican opponents outside the theater of war, he could order a full-blown investigation.
In many ways the Lorca case symbolizes Spain's attempts to deal with its painful past, with many, especially conservative groups, opposed to what they call opening up old wounds.
Lorca's niece said the family was reticent to open up the grave for several reasons.
"For one thing, the reality of not knowing for sure where it is," she was quoted as saying by El Pais. "But there are more. In the gorge there are between 1,000 and 3,000 dead. What happens to the rest? A partial exhumation would demean the real cemetery that holds so many victims of the same repression.
"We would not like for this partial digging to establish a difference between some victims and others," she added. "Right now they are all resting in a common cemetery, they have all been victims of the same savage and cruel murder."
She said digging up the grave would not uncover any new or vital piece of information regarding the poet's death.
Lorca, who was 38 when he died, is ranked as one of the world's most popular authors. His work deals with universal themes such as love, death, passion, cruelty and injustice.
Last year, Spain's Socialist government passed a watershed bill formally denouncing the Franco regime for the first time and made symbolic amends to victims of the war and the ensuing dictatorship.