Caoimhin Kelleher enjoyed a solid run in the Reds team earlier this season, but is now back on the bench.
With Alisson Becker fit, Kelleher is no longer the first choice, which Hallgrimsson admits is an issue.
“We would like our players to play,” he said, per the Irish Mirror. “I will answer this question the same way whoever it is; as a national team coach, you would always like to see your players playing.
“Whether it’s Evan or someone else. It’s our preference. We would like our players to play. The same with Caoimhin.
“We don’t know if he’s going to play games for Liverpool even though he’s done brilliantly. Should he go and try to play somewhere else?
“It applies to everyone. For a national team coach, of course you would like your players to be playing all the time.”