The owner has previously denied suggestions that he is to sell the club despite seeing his main assets crumble.
Landsbanki, his Icelandic bank was put into receivership last month, West Ham's shirt sponsors and another of Bjorgolfur investments XL Lesuire went bust in September and this week Samson Holdings filed for bankruptcy.
Vice-chairman Ausgeir Fridgeirsson told BBC Sport, "He is evaluating all of his business interests, including West Ham."
"West Ham is a well-run club with no debt and is one of Mr Gudmundsson's most important investments."