Bale was the star man in Real Madrid's 3-1 triumph over Liverpool in the Champions League final on Saturday, as the Welshman scored a brace that included a spectacular overhead kick and a long-range strike from outside of the box.
United were knocked out of the Champions League in the round of 16 by Sevilla, but Scholes believes that Bale could be the type of player to push Manchester United further in Europe.
"If [Jose Mourinho] can change something through the summer, buy new players and he can find a way of playing that maybe is a little bit more entertaining then who knows, you don't know,'" Scholes claimed at a UEFA Champions League final viewing party at Sky Garden in London.
"A lot can happen over the summer. Let's hope we can get close again. We need some good attacking players. I think the nucleus of the squad is quite good, there's some really good young attacking players. I think he possibly needs a bit of help with [Romelu] Lukaku. He seems like the only out-and-out centre-forward he's got.
"It's hard to know what's available, would Gareth Bale be available? People like Neymar will they be available? I don't know. These are the type of special players that I think United need. They'll have to improve massively to get anywhere near a final I think with the amount of top teams that are in the competition now, they don't look anywhere close to that at the minute."
Bale raised speculation over his future after comments he made following the final on Saturday night.