Having slipped down the pecking order at Old Trafford, it was expected that the Argentina international would be among those offloaded by the Red Devils in the last transfer window.
Premier League rivals at Goodison Park were prepared to offer the South American a fresh start in English football, but no deal was done, with Rojo figuring prominently under Ole Gunnar Solskjaer in pre-season.
He has since fallen back behind the likes of Harry Maguire and Victor Lindelof, and is aware that he needs to find regular football in order to cement a standing back in the plans of national team coach Lionel Scaloni.
Rojo told Ole: “I talked to Scaloni, he told me that he was happy because in pre-season I had played many games, that I looked good and that’s why he called me, but that I had to play.
“I’m sure that to play for the national team you have to play for your club, you have to always be there, and when you’re here, show why.”
With it looking like game time may be limited again at United in 2019-20, Rojo concedes that he may have to force the issue when another window of opportunity presents itself in the New Year.
The 29-year-old, who is capable of operating at centre-half or at left-back, added: “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.”
Everton boss Marco Silva admitted to the Liverpool Echo when the summer deadline passed that he had been hoping to get Rojo on board.
He said: “I don't like to go deeper into the deal and the business side of things. On the last day, he was one of the targets because the market is not so big at that moment and you don't have big, big time to do it also.
“At the end, and what I know through the feedback given to me, was that the clubs didn't agree. This is what I know.
“The player looks like he wants to come. I can't 100% say he wanted to come but he looks like he wants to come but at the end the clubs didn't agree.”
The Toffees may get a second opportunity to pursue Rojo in 2020, although United’s schedule is about to be stepped up and the South American could get outings across Premier League, Carabao Cup and Europa League competition.