According to reports, some institutional investors are proving to be reluctant to take part in the unusual bidding system devised by Google because they fear the share price could be set so high it will fall once trading begins.
There has also been little interest from individual investors, who have been put off by the high price.
Google's initial decision to go ahead with an auction-style IPO was linked in part to its desire to make its shares as widely available as possible.
This has led to the auction's underwriters suggesting privately that the IPO should not go ahead this week.
The Financial Times reports this morning that the IPO could now be delayed or even restructured to make it appeal to a wider group of investors. Other reports over the weekend said the entire process was hanging in the balance.
Google has warned that there may be no room for the share price, which will be set between $108 and $135, to rise in the period immediately following the flotation.
Another hitch in the process is the investigation by Californian regulators into Google's failure to register employee shares.
The public share auction is only open to US residents. People are still able to apply for a bidder number at a special Google .
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