The 29-year-old is part of his country's current squad but was an unused substitute in the overnight 0-0 friendly draw with Chile.
The defender, who can play either centrally or at left-back, believes Argentina boss Lionel Scaloni will only continue to select him for international duty in the future if he is regularly playing for United at club level.
Rojo, who has been at Old Trafford since summer 2014, has not featured for Ole Gunnar Solskjaer's side yet this season as Harry Maguire, Victor Lindelof, Luke Shaw and Ashley Young all appear ahead of him in the pecking order.
Axel Tuanzebe was also preferred on the bench for the opening game of the season against Chelsea and, while Shaw's injury has opened the door to possible game-time soon, he remained only an unused sub in the 1-1 draw at Southampton last weekend.
Eric Bailly would be another option for the United boss when he's fit, so Rojo appears to be struggling for regular action.
Rojo is well aware he needs to be playing first-team football at this stage of his career and admits he may be forced to seek a January exit if his situation doesn't improve.
The former Sporting Lisbon man was targeted by Everton in the summer but a deal couldn't be agreed between the clubs and now he will have to knuckle down and try and regain his place in Solskjaer's side.
He told news outlet Ole: "I'm sure that to play for the national team you have to play for your club. It's difficult to leave when you are at such a big club. I had the possibility of going to Everton, but due to the decisions of the club or the manager it wasn't possible.
"Now I have to fight until December and, if it doesn't work out, I will try to leave. The qualifiers and the Copa America are coming and I want to be part of that. I don't want to be out again, I want to exhaust all the possibilities and compete to be here."
Rojo, who has amassed 113 appearances for the Red Devils in all competitions, will hope to earn a recall or be in the match-day squad at least when the Premier League resumes next weekend when Leicester visit Old Trafford on September 14.