The Champions League-winning goalkeeper has confirmed he is leaving Paris Saint-Germain after being forced out of the side by manager Luis Enrique, who did not include the shot stopper in Wednesday’s UEFA Super Cup final against Tottenham, in which the French side won on penalties.
United and Manchester City have both been tipped to sign the 74-cap international.
When asked on the Wayne Rooney Show if Donnarumma should be a player area of focus for United manager Ruben Amorim, Rooney said: "Yeah, I think it has to be.
"I go back to when we had Roy Carroll and Tim Howard in goal. I don't think there was 100 per cent trust from the defenders in front of the two goalkeepers. But the minute (Edwin) Van der Sar comes in and calms everything down, the defenders trust him a lot more.
"(Andre) Onana's come in, he's a fantastic keeper, but he certainly didn't fill us with confidence last season.
"Donnarumma is 26, he's one of the best keepers in the world, it'd be crazy if Man United don't go for him. I don't think he's a risk."
Altay Bayindir replaced Onana in United’s opening game against Arsenal and performed poorly as the Gunners opened the scoring from a set piece and ended the game 1-0 at Old Trafford.
Donnarumma’s agent is now in talks for the Italy international to join City but after Rooney’s comments, Amorim may act quickly and go for the Italy international who would be a huge improvement on the side.