National football association (AFA) chief Armando Perez is to fly to Spain to speak to Atletico Madrid's Diego Simeone and Sevilla's Jorge Sampaoli.
And while in Europe he will sound out Pochettino, 44, Argentina FA sources told broadsheet La Nacion.
Ex-Argentina international Pochettino is contracted by Spurs until 2022.
Perez also plans to speak to Lionel Messi. He wants the Barcelona forward and former Argentina captain to reverse his recent decision to quit international football.
Messi made the decision last month after the national side lost to Chile on penalties in the Copa America final. Coach Gerardo Martino resigned a week later, reportedly over problems in naming a side for next month's Rio Olympics.
"It would be gratifying for everyone to persuade Messi to desist from his decision to quit," Perez told reporters.