Scholes suggests the former Liverpool midfielder along with four other high profile players.
In his column for the Independent, Scholes suggested that Manchester United need players for the here and now as well as for the future.
Alonso is one of four Real Madrid players on Scholes's wishlist along with Sami Khedira, Raphaël Varane and Angel Di Maria - along with Borussia Dortmund defender Mats Hummels.
He said: "I am sick of having to criticise the club to which I gave my life as a footballer. But this is a United team that lost seven league games at Old Trafford last season and began on Saturday by losing at home to Swansea. United need to arrest their decline. In those years under Sir Alex Ferguson, when trophy followed trophy, this sort of mediocrity was unthinkable. But it is happening.
"Looking at those five players, the obvious issue with Alonso for United fans would be his past with Liverpool. So what? He has that quality United lack. He is not the quickest but then he never was. Neither is Andrea Pirlo but he can play a bit. Alonso has a superb range of passing. He can shoot too. I noticed he signed a contract extension in January but, with Kroos as well as Luka Modric at his club, perhaps now would be the time he would consider leaving."
Liverpool fans would be hoping that such a move doesn't happen, and it is unclear that Alonso will want to move to United given his ties to Merseyside and the affection he says he holds for the club , along with the bond he had with the fans.
Some would also question why Alonso, like the rest of the players mentioned, would sacrifice the certainty of Champions League football for what appears to be uncertainty at Old Trafford this season. Even with illustrious signings, there would be no guarantees over them returning to the Champions League given how competitive it is towards the top of the table this season.
Otherwise, a player with great passing ability at the heart of their midfield that has experience of playing in the Premier League - as well as a terrific pedigree - it is a signing that would add a great to Manchester United. The chances of it happening, though, seem unlikely.