May, a double Premier League and FA Cup winner, who also won the Champions League, said Solskjaer's approach had been vindicated with the team's current resurgence.
“I think the way Ole's done it and the way he's looking at players, he's not going out and buying superstars like Di Maria or Falcao, who think they're something special," said May.
“He's going out and getting players who fit the Manchester United way, and Bruno (Fernandes) is that way.
“When those players come into the squad, you know they're not just here for the money, they're not just here for the ride, they're here to improve Manchester United.
“The way he's come in, he's been different class, and that gives everybody a boost.
“From the day he walked in, there's no ego about him, he's just a top player.
“He's improved the team and he makes other players play better. He's lifted the whole team.
“We've only seen him and Paul Pogba play for something like 219 minutes, but in that time they've scored or created eight goals and conceded none, which is incredible.
“You want to see that - and we will see that. It's only going to get better."