Zurich Financial indicated yesterday that, after a "detailed review", it will pull out of the auction the bank has convened for the sale - which it hopes, will net, around $14 billion.
RBS' insurance wing includes the Direct Line and Churchill brands, both popular among UK consumers.
Its sale would also provide a big boost for the bank's balance sheet - with revenue derived from it adding to the $24 billion earned by last month's record rights issue.
Asset writedowns suffered by the bank in the wake of the credit crunch are thought to have necessitated these moves, in order to avoid a funding crisis.
RBS chief executive Sir Fred Goodwin has previously indicated that offers have been "flooding in" for the insurance unit.
Other bidders for the business are currently thought to include German firm Allianz and US-based Travelers.