The former Formula 1 driver thinks that the only figure who can be at least fairly relaxed amid the situation is Stoffel Vandoorne.
"I predict a good career for him," the Australian is quoted by Spain's Marca.
"He's lucky to be with Fernando Alonso. Right now Fernando is in charge there and he's a great model for Vandoorne."
More generally, however, Webber is worried that Honda's reliability and performance crisis is endangering McLaren's very existence.
"That team does not exist to be 14th," he said.
"They have to find a solution very quickly because McLaren as a company could see their future threatened."
Amid the crisis, Webber's friend Alonso has elected to skip Monaco later this month to try to win the Indy 500.
"Alonso's decision to skip Monaco shows who's really running McLaren at the moment," said Webber.
"His relationship with them is clearly at a critical point. Honda has to raise its level of performance or McLaren will have to accept that a driver change is inevitable."
The season continues with the Spanish Grand Prix on Sunday.