Webber says the Spaniard is "a long way away from where he wants to be".
Alonso, in his third year with the Woking-based team, has endured a torrid pre-season after the Japanese manufacturer's new engine failed to live up to expectations. The two-time champion, who was hoping to fight near the front this year, qualified 13th for the season-opening Australian Grand Prix, retiring from the race with a damaged floor.
Alonso's contract with McLaren expires at the end of the year, but his close friend Webber suggested the Spanish driver's frustration could lead him to leave before the year is over.
"Maybe Fernando is not there the whole year," the Australian told Belgian broadcaster Sporza. "Maybe Stoffel [Vandoorne] has a different teammate at some point. Fernando might not do the whole year, you never know. He's frustrated. He doesn't even want to finish seventh or sixth. Maybe points for Stoffel is quite nice. Fernando is not interested in points. He wants to fight for the podium, so Fernando is mentally a long way away from where he wants to be," Webber added.
Tough year not bad for Vandoorne
Webber, a nine-time grand prix winner who retired from the sport at the end of 2013, believes Alonso's teammate Stoffel Vandoorne is in a different situation and could still benefit from a difficult season.
Vandoorne, competing in his first full season in F1 this year, finished 13th in Australia, two laps down.
"It's a tough situation, the car and the team are not there," Webber added. "But in a way he can still do the learning in the background, so it's not a bad scenario for him to learn the first season in Formula 1 because the radar is not on him."
"The radar is on the team and the politics and the problems with Honda."
"He has such good pedigree in junior categories, I think there's still good currency for him. You can't have two years like this, but he will be okay."