But the national team boss will also work with Cooney-Cross, one of Australia's most gifted players, to have her firing in time for the Asian Cup.
Cooney-Cross has started just one game for Arsenal this season - and played just 110 minutes across four appearances - with Mariona Caldentey, Kim Little and Frida Maanum ahead of her.
"In the end, each individual has their own information and where they want to be and what they want to do, and we can only assess Kyra in her situation at the moment," Montemurro told AAP.
"We know that being at Arsenal and having a pretty good connection with them, we know that she's in a very good environment.
"We know that there's a lot of games coming up because they (have started) their Champions League campaign. So we're confident that she'll be part of the rotation of the group.
"She also understands that she's got Kim Little and Mariona fighting for that position.
"So it isn't easy and Kyra's at that point now where there is that real adjustment from 'I'm at a big club, 25 top players challenging for the Champions League' so on and so on.
"So it's more understanding, 'OK, well, I'm in this situation, I'm in a big organisation where there's lots of competition' and it's that mental strength."
Montemurro noted Cooney-Cross, 23, could consider a loan or transfer - but that wasn't necessarily the best option.
"It'd be quite easy for her to go to a lesser club and get game time," he said.
"But I think she has to decide whether the training stimulus and being in a top environment, as opposed to being in a situation where you're going to play regularly and probably the challenges aren't there. There's a different mental state to that.
"So at the moment, I think the challenge is a positive one, it's a good one because she's in a big, big environment and that's where she'll shine as a professional."
Cooney-Cross is set to run the Matildas midfield for upcoming friendlies against Wales and England.
She has a great relationship with returning veteran Katrina Gorry, and is building chemistry with Clare Wheeler, Winonah Heatley and Amy Sayer.
"She's obviously a fundamental midfielder as part of the group," Montemurro said.
"Her individual qualities, but also what she does for the team in terms of positioning, in terms of starting the play, in terms of her initiating a lot of the forward scenarios.
"We're working a lot with her defensive positioning at the moment, and where we believe she can be more effective.
"So she's obviously an important player going forward, and even as a character, she's really, really important to the group.
"So we'll assess her situation on a week-to-week, day-to-day sort of scenario, where she's at, and make sure that she's always prepared mentally to understand where she's at and the challenges ahead of her."
21°C