The Scot thought that the then Bayern Munich midfielder could replace United legend Paul Scholes.
Real Madrid's Toni Kroos
The Scot even went so far as to suggest the Germany international and current Real Madrid star would have been the perfect replacement for United legend Paul Scholes, who retired from playing just before Moyes took charge.
The former Everton and Old Trafford boss is widely considered a poor appointment by the Manchester outfit, taking a side who won the Premier League in 2013 under Sir Alex Ferguson to what would end up being a seventh place finish the following year.
Manchester United Manager David Moyes dejected
Moyes himself was sacked before he saw the end of his one season at United, but the direction of the Red Devils' campaign was already established, with interim manager Ryan Giggs only overseeing a handful of games at the end of the season.
And though there are several Moyes signings that are looked at with some derision, none more so than former Toffees favourite Marouane Fellaini, who arrived for a huge £27.5 million fee (BBC Sport) but has scarcely provided form worthy of that price tag, Moyes' comments on his wish to secure Kroos for the Premier League giants could have been the sort of transfer that could have saved either his, or Louis van Gaal's, tenure.
Belgium's Marouane Fellaini
"I wanted to bring Kroos to Manchester United, from Bayern," Moyes said in the Times. "I thought his range of passing and his ability to play people in would have made him a top United player, maybe Scholes' heir. He's gone on and shown at Real Madrid what a fantastic footballer he is.
"Kroos is a special talent, probably the closest thing at [Euro 2016] to a Xabi Alonso, an Andrea Pirlo or Paul Scholes. It's the number of times he gets on the ball, his vision, his choice of when to play long or short.
"He's got a great array of passes and the big thing for me is he tries to make winning passes. He tries to make passes that play teammates through. He's not one who just goes sideways and backwards."
Germany's Toni Kroos (L) and Ireland's Marc Wilson in action
Many who would have watched United under Van Gaal, Moyes' eventual replacement at Old Trafford, would think that a playmaker like Kroos was just what United were missing for much of the past season. The Red Devils had one of their lowest "goals for" totals in years, and were accused of lacking attacking quality.
With uncertainty regarding Kroos's situation in Madrid, it may be that the former Bayern man is on the move again, and new United boss Jose Mourinho could do a lot worse than trying for the German a few years after one of his previous predecessors did the same.