United are particularly angry at the timing of Ronaldo's interview with Piers Morgan, during which he said he "doesn't respect" Ten Hag, coming just hours after the team had made a point of demonstrating their team spirit and togetherness with a dramatic win at Fulham on Sunday.
United said in a statement on Monday: "Manchester United notes the media coverage regarding an interview by Cristiano Ronaldo. The club will consider its response after the full facts have been established.
"Our focus remains on preparing for the second half of the season and continuing the momentum, belief and togetherness being built among the players, manager, staff, and fans."
Sources have told ESPN the club are keen to keep the emphasis on what they believe was a significant victory at Craven Cottage, secured thanks to Alejandro Garnacho's stoppage-time goal.
Privately, however, the club are disputing a number of points raised by Ronaldo.
The 37-year-old claims United and Ten Hag wanted to "force him out" in the summer, but sources have told ESPN that during the transfer window, United were made aware that the striker's representatives were actively looking for a move away.
United have also taken issue with Ronaldo's claim that their Carrington training base has not been updated since he was last at Old Trafford.
Sources told ESPN that the pool, canteen and recovery areas have all been revamped, while more than £200,000 was spent to build a state-of-the-art analysis and meeting room at the specific request of Ten Hag.
Sources told ESPN that United will leave Ten Hag to deal with Ronaldo's latest indiscretion, with the backing of football director John Murtough and chief executive Richard Arnold.
Ten Hag took the lead when Ronaldo refused to appear as a substitute against Tottenham in October, choosing to suspend the Portugal international from first-team training and making him unavailable for the 1-1 draw with Chelsea.
Some sources close to the club believe Ronaldo's interview was designed as a "power play" to force a move away from Old Trafford in January while also negotiating a financial settlement for the remaining months of his contract, which runs until June. United have been open to letting Ronaldo leave for free since the summer but have been reluctant to agree to a payoff.