The former Boro manager returns to United where he was Sir Alex Ferguson's long time assistant.
Speaking ahead of the 360 Sports TV Masters Cup, Downing said: "The one thing I will say about McClaren is that he's a very good on-field coach, and I think that team does need coaching a little bit.
"When I watch United they're so ill-disciplined, and [McClaren] is really good at organising the team and getting them how he wants them to play, and I'm sure he and Ten Hag have got the same sort of ideas.
"We were a very well organised as a team. McClaren overachieved with us, instilled a winning attitude, we got to the UEFA Cup final and beat some amazing teams just by pure hard work and being very well drilled."