Louis van Gaal named the 24-year-old among his desired transfer targets ahead of confirmation of his appointment at Old Trafford, however Kroos has since insisted a move is not in the offing.
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"I love watching Toni Kroos. I think he's brilliant," Scholes wrote in his blog for Paddy Power.
"I love the way he controls the ball and controls games. He can really play a pass and has superb vision. Kroos is capable of scoring goals too, from outside the box on either foot.
"I just wish Manchester United had signed him. Yes, it is good to see United bringing in new players, but they haven't signed anything like the quality of Kroos."
Germany marched into the World Cup last-16 stage by topping Group G and face Algeria on Monday evening for a place in the quarter-finals.
Scholes praised Joachim Low's tactical approach but raised questions over Germany's defence - namely Per Mertesacker and Benedikt Howedes.
"Joachim Low’s strategy of using four centre-backs has managed to keep to clean sheets in the group games for Germany. However there are weaknesses in his team," he continued.
"He must be doing something right with more than 100 caps but Per Mertesaker is slow and cumbersome.
"At left-back the Shalke centre-half, Benedikt Howedes, looks a little vulnerable. Mats Hummels is not the quickest either."