The German World Cup-winner went on to join Real Madrid, but the player has confirmed he was prepared to move to the Premier League from Bayern Munich.
Speaking to GQ magazine (h/t lifePR, via Marcus Banks of the Manchester Evening News), Kroos said he told Moyes he would transfer to United after being impressed by Sir Alex Ferguson's successor.
"I knew before that Manchester wanted me. And Moyes underlined that absolutely. It was a really nice afternoon with very nice people. We talked a lot about United's footballing plan which convinced me. In the end, we agreed to do it. We agreed verbally.
"I am not somebody who worries about contingencies. Yes, it was close. I almost went to Manchester United. But it did not happen that way."
Kroos eventually penned a six-year deal with Los Blancos that summer and went on to win La Liga and three UEFA Champions League titles.
United have fallen from grace since Ferguson's retirement, with Louis van Gaal and Jose Mourinho both unable to revive the club's fortunes after Moyes' managerial sacking.
Kroos added he has no regrets about turning his back on a move to England:
"One thing I can say for sure: Manchester United would not have won the Champions League three times. Manchester United is not a club you go to for a short while. Manchester United is too big for a year or two. This is not a club to end your career.
"Since both the player and the club must have a clear idea—I signed with Real Madrid until 2023."
United have continued to have issues in midfield since missing out on the German's capture, despite the then-world-record signing of Paul Pogba in August 2016. The Red Devils paid €110 million (£93.2 million) for the Juventus superstar, according to Ed Aarons of the Guardian.
Pogba has helped United to victories in the UEFA Europa League and Carabao Cup, but the Manchester giants have failed to live up to expectations in the Premier League.