"Unfortunately the fire in his car pretty much rules him out in qualifying," Bell told Sky Sports. "We'd never get it out in time, so yes, he'll miss qualifying.
"It looks at this stage as though it was a high-pressure fuel leak probably from the pump on the engine and when that catches fire it's quite a big thing.
"It could have been (a lot worse) but fortunately it wasn't."
Saturday's setback continued a bad run for Palmer, who crashed during Friday's practice session.
"There's no time frame on (Palmer's future with Renault)," added Bell. "We want Jolyon to succeed.
"If you look back at last year, he was under pressure at the start of the season with (former Renault driver) Kevin (Magnussen) and by the end of the season he was regularly in front.
"We just need to see a level of progression by the end of the season."
Palmer, who finished 18th with one point during the 2016 season, has yet to score this campaign. In contrast, team mate Nico Hulkenberg has scored 18 points.
(Reporting by Ed Dove, editing by Pritha Sarkar)
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