Valencia called up by Ecuador for Copa America
The 33-year-old's inclusion has received criticism in some quarters as Valencia has played less than 10 matches in an injury-ravaged season.
"There are players who haven't played much but they are players that you know will be important when they're in the national team," said Gomez.
"I'm not going to throw out Valencia until he tells me he's quitting."
Valencia, 33, is the Ecuador captain and has won 94 caps, scoring 11 goals.
Although he spent the last few years of his Old Trafford career as a right back, Gomez said he sees Valencia as a right winger, the position where he made his name and earned a move to United after a string of sparkling displays at minnows Wigan Athletic.
Ecuador have been drawn in a tough Group C at the Copa America hosted by Brazil, where they will face holders Chile, record 15-time winners Uruguay and guests Japan.
Their first match will be on 16th June against Uruguay in Belo Horzonte.
Ecuador are one of only two of CONMEBOL's 10 member nations never to have won the Copa America, alongside Venezuela.
Their best finishes were fourth in 1959 and 1993, both times as hosts.
Goalkeepers: Alexander Dominguez (Velez Sarfield/ARG), Maximo Banguera (Barcelona), Pedro Ortiz (Delfin)
Defenders: Gabriel Achilier (Monarcas Morelia/MEX), Arturo Mina (Yeni Malatyaspor/TUR), Robert Arboleda (Sao Paulo/BRA), Xavier Arreaga (Seattle Sounders/USA), Pedro Velasco (Barcelona), Jose Quintero (Liga de Quito), Cristian Ramirez (FC Krasnodar/RUS), Beder Caicedo (Barcelona)
Midfielders: Jefferson Intriago (Liga de Quito), Jefferson Orejuela (Liga de Quito), Jhegson Mendez (Orlando City/USA), Carlos Gruezo (FC Dallas/USA), Andres Chicaiza (Liga de Quito), Renato Ibarra (America/MEX), Antonio Valencia (no team), Romario Ibarra (Minnesota United/USA), Ayrton Preciado (Santos Laguna/MEX)
Forwards: Enner Valencia (Tigres/MEX), Angel Mena (Club Leon/MEX), Carlos Garces (Delfin)