There has been no confirmation of the deal from Glasgow but media reports in Argentina claim the move for the international winger will be tied up when visa arrangements are completed.
"I am going to play for a season in Scotland. We agreed for nine months with an option for a year more", José María Núñez Piossek told the newspaper La Gaceta.
He added: "The level of play is good, the league is very professional and I am very pleased with this opportunity."
If the move goes through José María will team up with fellow-Puma Bernie Stortoni.
He has played in England with Bristol and in France with Castres Olympique and Bayonne. He has been playing for Huirapuca in Argentina and was in the Pumas squad that faced Scotland during the summer.
A prolific try-scorer, José María represented Argentina in the 2003 Rughy World Cup but missed out on the 2007 competition - a knee injury forcing his late withdrawal from the Pumas squad.