Martino, whose club side is on course to collect the MLS Supporters' Shield with two matches of the regular season remaining, has previously done little to downplay speculation about him taking the reins of Argentina or Colombia instead.
Ricardo "Tuca" Ferretti is the interim manager of Mexico for the upcoming friendlies against Costa Rica and Chile as the search for a new head coach continues after Juan Carlos Osorio stepped down in July.
"I think he is a great coach, so hopefully he can come and it will be the best for the national team," Lozano told reporters on Sunday, according to Marshall.
Martino, 55, has never worked in Mexico, but has proven his adaptability through stints in various South American countries, Spain, and the United States during his playing days and managerial career.
The rumors that Martino will take the helm strengthened on Monday when former Chivas de Guadalajara boss Matias Almeyda was confirmed as new head coach of the San Jose Earthquakes for the 2019 MLS season. His name featured prominently alongside Iran handler Carlos Queiroz for other managers apparently in the frame for the Mexico gig.
Mexico hosts Costa Rica in Monterrey on Thursday before entertaining Chile at Queretaro FC's Estadio Corregidora five days later.