Neither player has started a Premier League match this season, with Dutch forward Zirkzee playing only 82 minutes in the top flight, while England midfielder Mainoo has totalled 138 minutes since August.
Both players have fallen out of the picture with their national teams, and British media have reported the pair are looking for moves in the January transfer window to reignite their chances of playing at the June 11th to July 19th World Cup in North America.
"I was a football player. I understand everything, and I want to help my players in every situation," Amorim told reporters ahead of Monday's league match against Everton.
"I want my players to be happy. I understand the frustration of some players, seeing that the World Cup is there, and I know what it means for the World Cup, but Manchester United comes first.
"So if I can help the club and the players, I will be happy, if not I have to think about the team. The club comes first, so we have to think about the club and the team, and then everything can happen."
Both Mainoo and Zirkzee could see more playing time at United in the coming weeks, with Bryan Mbeumo and Amad Diallo set to leave for the Africa Cup of Nations next month and with striker Benjamin Sesko picking up an injury.