ACE Bermuda and XL Capital are set to drop out of the billion dollar legal battle over whether the destruction of the World Trade Centre resulted from one attack or two.
Leaseholder Larry Silverstein is fighting to prove the 11 September tragedy should be considered two insured events.
Insurers want a legal ruling that it was one.
If Silverstein wins, he could make two $3.55bn (£2.4bn) claims - a total of $7.1bn (£4.9bn).
ACE and XL are among 22 insurers with exposures to the building, but used different policy wordings from the others, it was reported.
Their policy wording meant they provided cover for just one event.
AM Best, the insurance ratings agency, reported a Silverstein lawyer as saying Silverstein was close to reaching an agreement with ACE and XL Capital.
The two companies used a form written by broker Willis.
This specified that "occurrence shall mean all losses or damages that are attributable directly or indirectly to one cause or to one series of similar causes.
"All such losses will be added together and the total amount of such losses will be treated as one occurrence irrespective of the period of time or area over which such losses occur."
The unnamed attorney was reported as saying the "vast majority" of the other insurers had based the terms of their cover on an alternative policy, which did not define "occurrence."
