The foundation's financial troubles have been attributed to the continuing weakness of the US stock market, which has led to a sharp drop in donations and endowments to New York's cultural institutions.
The fall in the number of tourists visiting the foundation's galleries and museums since the 11 September attacks is thought to have added to its difficulties.
To make ends meet, the Guggenheim has cut half its staff, reduced its exhibition programme and opening hours and shut galleries in the SoHo area of New York and a casino in Las Vegas.
The Guggenheim's flagship museum in New York remains open, as does the Hermitage Museum in Las Vegas and museums in Berlin, Bilbao and Venice.
Talks on proposals for a £90m gallery in Rio de Janeiro, Brazil, are going ahead.