The second-placed team in the Primera Division are looking at strengthening their squad in an effort to stay in the upper reaches of the league, and the former Liverpool and Galatasaray man Insua is who head coach Diego Simeone has turned to fortify his defence, with the 24-year-old needing only to pass a medical before the deal is completed.
Atletico announced on their website that Insua would be joining them.
The Spanish club said in a statement: "Atletico Madrid and Sporting of Portugal have reached an agreement for the transfer of Emiliano Adrian Insua to the 'red and whites'.
"The Argentinian full-back will sign for the rest of the season and three more once he has passed the medical."
Insua joined Liverpool from Boca Juniors as a teenager in January 2007 but after being unable to hold down a regular place in the first team at Anfield he was allowed to join Galatasaray on loan in 2010.
That did not develop into a proposed permanent move, but Sporting Lisbon stepped in to take him to Portugal in summer 2011.
He has been capped by Argentina and had established himself as a regular in the Sporting side over the past 18 months.