According to the magazine’s report, Mr. Dolan used the last week’s meeting to stress his business interest in having the Rockettes perform at the inauguration.

“I don’t believe it’s going to hurt the brand,” he was quoted as saying. “And nobody is more concerned about that than the guy sitting in this chair. I’m about to spend $50 million remounting this summer show. I’m going to spend a similar amount remounting next year’s Christmas show. I gotta sell tickets.”

Since the decision in late December to have the Rockettes perform, the dancers have been the subject of intense scrutiny. A debate has been waged over whose decision it was to have the dancers perform and whether they had any choice in the matter. The Rockettes are among only a few acts who’ve signed on. Others include the singer Jackie Evancho and the Mormon Tabernacle Choir.

The Madison Square Garden Company has maintained that part-time dancers can choose whether to appear at any event, and has decided to let full-time dancers opt out of performing at the inauguration, even though they were told by their union, the American Guild of Variety Artists, that it was mandatory.

“This is the one time we’re going to do this,” Mr. Dolan reportedly said of that exemption in the meeting. It was not clear how many Rockettes were present.