Questions have been raised over the influence of Barker and her husband Michael Auer, who was working voluntarily with the company. They also work for the Michigan-based Grand Rapids Ballet Company, and hired a couple from that company in roles that were reportedly not advertised locally.
The company receives about $5.4 million in funding from the Government each year.
"I am certainly keeping an eye on the issue," Ardern said this afternoon at her post-Cabinet press conference.
"I've asked for briefings from the Ministry of Arts, Culture and Heritage. I take a keen interest in making sure we have a successful Royal NZ ballet company.
"I want to see whether or not it can be worked through with those involved at a senior level first."
Ardern said the pathways into a career in the arts could be improved.
"What we're doing to support the flow of New Zealand dancers is equalling something we should turn our minds to.
"We've talked about trying to improve those pathways across the arts and culture sector through things like apprenticeships, which we don't tend to have entrenched as much in that sector.
"I do think there's opportunity for there to be training in the field, using the New Zealand School of Dance."
In a letter to stakeholders and released to the media, Steven Fyfe said that 10 dancers had left the company since Barker came on board, including three retirements.
He acknowledged that supporters had raised concerns about the direction of the company, and asked for feedback. A forum would be held early next year to discuss options.
"Doubt has been expressed by some about our commitment to providing opportunities for New Zealanders. The RNZB has always been a blend of ballet talent from New Zealand and the rest of the world," he said in the letter.
"We are as committed as ever to nurturing New Zealand's creative talent ... Equally, Patricia is committed to seeking New Zealand talent to join the RNZB."
He said the company offered three 2018 contracts to students from the New Zealand School of Dance. Two joined overseas companies, while Luke Cooper will be joining RNZB as the 2018 Todd Scholar.
"We are ending 2017 in good heart, looking back on a year in which we have achieved notable artistic milestones."