The Championship side are the subject of a winding-up petition from HM Revenue & Customs.
"The publicised investment into the club from a California-based group has unfortunately failed to materialise as promised," a club statement said.
"No money whatsoever has been forthcoming in this regard."
The Exiles said they had agreed a deal with the group in early September, having avoided liquidation by settling a previous debt with HMRC.
In October, an insolvency court granted the Richmond-based side an adjournment on their most recent winding-up order for "a number of weeks".
Welsh said then that they were "confident" they would be able to settle the debt, but the Exiles are now carrying out a "full and comprehensive strategic review" of the club's future.
"All options are currently on the table," the club statement added.
"The club's board are open to approach by any parties or individuals interested in taking London Welsh forward."
The Exiles were in the Premiership as recently as 2015, when they were based at the Kassam Stadium in Oxford and finished bottom of the table after losing all 22 games.
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London Welsh's future is back in doubt as the club have not received investment proposed by a United States-based group.