The Red Devils have been linked with a move for England midfielder Rice in recent months.
However, former United stalwart Butt thinks that Ole Gunnar Solskjaer already has enough quality in midfield to avoid spending big on Rice.
Speaking exclusively to Ladbrokes at the launch of their European Championships 5-a-side Bet, he said: “I think Man United are solid enough in midfield.
“I keep hearing things about Declan Rice, but is he a better player than Scott McTominay? I’m not sure; I think with McTominay, Paul Pogba and obviously Bruno Fernandes, we’re in a good place in the middle of the park.”
Instead, Butt wants to see United spend that cash on finding a world class partner for Harry Maguire at the heart of the defence.
Victor Lindelof filled that role last season, but looked a little shaky at times, and there is now talk that Maguire needs a pacey partner to compliment his physically domineering style but lack of speed.
Real Madrid’s Raphael Varane has been linked with a move, but at 28 there are concerns that a big fee may not represent the best value.
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However, Butt rejects that view, insisting that ex-United striker Teddy Sheringham’s treble-winning exploits showed that age doesn’t always matter if it gets results.
“For me, next season has to be about getting some silverware back in that trophy cabinet for Manchester United,” Butt went on.
“It’s about getting the right players who will allow you to challenge for trophies. It’s a winning club, so we can’t go this long without silverware.
“The biggest thing that needs addressing for me at Manchester United this summer is that centre-back position; we need a partner for Harry Maguire. It has to be someone that’s going to be compatible with Maguire.
“If you spend the kind of money you did on Harry Maguire, you then have to follow it up by bringing someone in who can play with him.
“He’s the club captain; Victor Lindelof is too similar to him. It needs to be someone with pure, blistering pace, someone who can play out from the back.
“Everyone talks about Raphael Varane. I understand he’s a little bit older than most people would perhaps like, but you just have to go back to the days of Teddy Sheringham.
“I think we bought him when he was 32, and we went and won the treble with him. If Varane is available, then I’d go all out for him.”