Yahoo's board has been meeting to consider the offer and look at alternatives, including the sale of Yahoo's advertising business to Google or a possible merger with AOL.
Previous talks of a merger between Yahoo and AOL broke down when neither side was able to agree a price.
Although Microsoft's offer represents a 62 per cent premium on Yahoo's current value, Yahoo's board apparently feels that it undervalues the company as it reflects a five-year low of the stock.
Yahoo has suffered eight consecutive quarters of profit decline, and a loss of market share in the search arena to Google.
It is believed that the Yahoo board has decided to dismiss any offer of less than US$40 per share, which means that Microsoft would have to up its offer by around US$12 billion before Yahoo would seriously consider the acquisition.
Regardless of the outcome, many analysts are predicting that any merger will raise antitrust concerns, meaning that it may be some time before a final judgement is reached.