Former England international Scholes retired at the end of last season, leaving a big void in the centre of the Red Devils' midfield.
And Beckham, who played for the LA Galaxy as they lost to Manchester City 7-6 on penalties on Sunday night, believes Inter Milan's Sneijder - who has been heavily linked with a move to Old Trafford - could be the man to fill it.
He said: "Scholes is the one player they want to replace. He is such a great talent and he will be missed. They're going to have to get someone special.
"There's a lot of talk about Wesley Sneijder. He's such a talented player, a great guy as well. I'm sure he would fit right into a United team."