Tuchel’s side head to Old Trafford looking to cement their grip on third place in the Premier League, while sixth-placed United appear certain to miss out on a top-four finish.
United interim boss Rangnick fears Erik ten Hag, the Ajax coach who will take charge at Old Trafford from the end of this season, will have to significantly overhaul his squad to make the club competitive at the highest level.
In contrast, Tuchel is confident Chelsea’s needs only run skin deep despite an inconsistent season marred by Russian owner Roman Abramovich putting the club up for sale following the British government’s sanctions on him after the invasion of Ukraine.
Still waiting for the sale to be completed, Tuchel has potentially lost ground on Chelsea’s rivals in planning for signings once the transfer window reopens.
Antonio Rudiger is expected to leave for Real Madrid on a free transfer this summer, with fellow centre-back Andreas Christensen reportedly bound for Barcelona.
Asked what Chelsea need this summer in light of Rangnick’s heart operation comments, Tuchel replied: “Cosmetic surgery. I would be less concerned if we had still the same ownership, if we could rely on our structure.
“As this is also in question we are, not concerned, but aware of the danger that the situation is maybe a bit more complex.
“And it can be complex enough if you lose a player like Toni, and maybe lose another player like Andreas with the kind of quality, and both of them free…
“It can be demanding enough even if everything else stays in place. So with this in question it can be a very, very demanding summer.
“I don’t know if surgery is the right term for it but I just want to be positive about it and stick to the things we can influence.”