The defender has struggled to break into the first team this season.
The Argentine defender started the first two games of the campaign under Koeman but quickly made way when Ashley Williams was brought in from Swansea City.
He then missed the following seven games of the season as the Welsh captain formed a solid defensive partnership with Phil Jagielka.
Tottenham's Erik Lamela in action with Everton's Ramiro Funes Mori
He returned when Jagielka was rested for last weekend’s home clash with West Ham United and was largely impressive as the Blues secured a 2-0 win.
It does not guarantee him a place for Saturday’s away trip to Chelsea and Koeman says the Argentina international has accepted that fact.
“In the beginning, it was difficult because sometimes it’s strange if you play for your national team and you play with Messi and all the big guys, and you don’t start at your club,” he told the Liverpool Echo.
“I spoke several times to him and I said: ‘Wait, you need to wait. This is the team and the team is doing well. We are defending well and I have no reason to change. But keep going, keep training well and hard’.
“In the beginning that was a little bit difficult for him but after that time he did his training how he needs to do his training.”
Everton's Ramiro Funes Mori looks dejected
It remains to be seen if Ramiro Funes Mori remains in the Everton first team picture moving forward.
Phil Jagielka has struggled to impress in recent weeks with several disappointing performances leading to calls for him to be dropped.
That happened last week with Funes Mori replacing him and given the Argentina impressed and helped his team to a clean sheet, it would be surprising to see Koeman change this weekend.
Everton's Seamus Coleman and Ramiro Funes Mori in action with West Ham United's Michail Antonio