The bucardo became extinct in 2000, but cells from the last animal were frozen in liquid nitrogen.
In 2003, a cloned calf was brought to term but died a few minutes after birth.
Now, the scientists will test the viability of the female bucardo's 14-year-old preserved cells.
The bucardo, or Pyrenean ibex, calf born through cloning was an historic event: the first "de-extinction", in which a lost species or sub-species was resurrected.
The Aragon Hunting Federation signed an agreement with the Centre for Research and Food Technology of Aragon (CITA) in Zaragoza to begin preliminary work on the cells from the last animal, named Celia.
One of the scientists behind the cloning effort, Dr Alberto Fernandez-Arias, told BBC News: "At this moment, we are not initiating a 'bucardo recovery plan', we only want to know if Celia's cells are still alive after having been maintained frozen during 14 years in liquid nitrogen."
In addition to this in vitro work, they will also attempt to clone embryos and implant them in female goats.
"In this process, one or more live female bucardo clones could be obtained. If that is the case, the feasibility of a bucardo recovery plan will be discussed," Dr Fernandez-Arias, who is head of the Aragon Hunting, Fishing and Wetlands Service, explained.
The bucardo (Capra pyrenaica pyrenaica) was a sub-species of ibex, with distinct physical and genetic characteristics to other mountain goats inhabiting the Iberian Peninsula. It was perfectly adapted to life in its mountain habitat, and to survive the extreme cold and snow of winter in the Pyrenees.
However, its population had been declining for years for several reasons, including hunting. In April 1999, researchers captured the last animal, a female named Celia. They obtained skin biopsies and froze the tissue in liquid nitrogen at a temperature of -196C (-321F).
The following year, Celia was killed by a falling tree in the National Park of Ordesa in north-east Spain. But a team including Dr Fernandez-Arias, Jose Folch and others were able to inject nuclei from Celia's preserved cells into goat eggs that had been emptied of their own DNA.
Then they implanted the eggs into surrogates - hybrids between Spanish ibex and domestic goats. Of 57 implantations, seven animals became pregnant and one was carried to term.
The baby bucardo was born in 2003 - the first successful "de-extinction". But the clone of Celia died a few minutes later due to a defect in one of its lungs. Earlier this year, Dr Fernandez-Arias related the story in a TEDx talk, as part of a meeting on de-extinction.
Even if the new effort succeeds in producing healthy clones, any future recovery plan for the bucardo would be fraught with difficulty - especially given the only frozen tissue is from a lone female.
One possible approach for bringing back the bucardo might be to cross a healthy female bucardo clone with a closely related sub-species - such as the Spanish ibex (Capra pyrenaica hispanica) or the Gredos ibex (Capra pyrenaica victoriae) - and then selectively breeding the offspring to enhance traits typical of the bucardo.
Several other possibilities could also be explored. For instance, researchers have been able to reverse the sex of female mouse embryos by introducing a key gene that makes them develop as males.
In addition, George Church, professor of genetics at Harvard University, explained that a technique known as Crispr opened up new opportunities in the field of endangered species conservation and de-extinction. The technique allows researchers to edit genomes with extraordinary precision.
Such "genome editing" techniques could be used to introduce genetic diversity in populations that are so closely related it poses a threat to their survival.
"In some cases, you have a hunch as to what diversity is needed. You might specifically want diversity in the major histocompatibility complex [a large gene family involved in immune responses]," Prof Church told BBC News.
"For example, part of the problem with the Tasmanian devil is that they are so closely related in terms of their immune system that they have problems rejecting the facial tumour cells that they spread by biting each other."
However, he said, such techniques might eventually offer a way to extensively edit the genome of an Asian elephant to make it more like a mammoth, using a genetic sequence from the extinct animals.
Commenting on plans for the bucardo cells, the Aragon Hunting Federation said it wanted to "develop initiatives in the field of ecology in order to defend the natural environment".
The sum provided to fund the research at CITA has not been disclosed.
Paul.Rincon-INTERNET@bbc.co.uk and follow me on Twitter
Scientists in Spain have received funding to test whether an extinct mountain goat can be cloned from preserved cells.