Ronaldo has scored four times in three appearances for the 20-time English champions since returning to the club from Juventus in the latter stages of the summer transfer window.
The 36-year-old is believed to be targeting at least another four years as a player, but Sherwood has claimed that the Portugal international could replace Solskjaer as manager of Man United in the near future.
"We've seen him do it on the international stage, most recently at the Euros, barking out orders. That boy will be a manager 100%. I would have a bet on him being Manchester United manager in 18 months," Sherwood told Ladbrokes.
"Whenever Ronaldo finishes playing I think he will become a manager, it will be an automatic choice. If they win the Premier League, Champions League, FA Cup, any of those trophies, then Solskjaer keeps his job. But if they don't win anything I think they've got a manager there in the making.
"He could bring an experienced coach in there with him - someone like Carlos Queiroz - as he'll know plenty of them. And I can see him being a manager at Man United in the future. He's almost coaching now; you saw it at the weekend during the warm-up whispering in [Raphael] Varane's and [Harry] Maguire's ears.
"But I don't think it's that he needs the captain's armband to be a leader, he leads by example anyway. He did when he was at United the first time it's just now he's being more vocal with it."
Ronaldo was left out of the squad for Wednesday's EFL Cup clash with West Ham United, which the Hammers won 1-0 to progress to the fourth round of the competition.