They both think Atletico Madrid manager Diego Simeone should be in charge at Old Trafford next season.
Simeone's team ousted the Red Devils from the Champions League in the round of 16 thanks to Renan Lodi's 41st minute header. Thanks to the goal, the Spaniards won 2-1 on aggregate following a 1-1 first-leg draw.
With the likelihood of Ralf Rangnick leaving the club next season, the question of who will replace him has become urgent. United stalwarts Keane and Scholes have both weighed in on the matter.
Keane admitted last month he wanted Simeone to succeed Rangnick at Old Trafford. "The suitable manager" should be found, regardless of whether he is employed elsewhere.
"Get the manager you want," Keane said in February at Overlap Live. "You need go hire the right manager for your club." People say 'oh, someone has a club'. But if you genuinely want a manager – or a player – you go get him.
"Forget about his two-year absence. Why not a manager? If you think he's the right manager for Manchester United, go get him. You go pay whoever it is. "They need to find the appropriate manager."
"Perhaps Simeone is the proper character. Atletico is having problems with him. Maybe he's joined them. Get him, Simone, he's a big character. He's done well.
"He has a tremendous personality. He is not a player's player. Maybe he could join the club. It may change soon. I don't think it's all doom and gloom at United, but they need to get the manager. "If the manager is wrong, everything else falls apart."
Scholes, who was a post-game analyst for BT Sport, mirrored his former teammate's thoughts. "If Diego Simeone was managing them, United would have won that game," he said.
Atletico Madrid held their hosts at bay for the bulk of both games, though United had more chances in Manchester than in Madrid.
United's chances of winning a trophy are now little to none. The club's trophy drought continues, with the 2017 Europa League their last big win. For a club of United's stature to go so long without a trophy is inexcusable.
Alphonsus Odumu 1 w
Really