It has threatened to lower its $44.6bn (£22.5bn) offer and replace the Yahoo! board with its own directors if Yahoo! does not acquiesce.
According to a report in the Wall Street Journal, Yahoo! is expected to respond today with its own letter saying that it is not opposed to a deal in principle, but that Microsoft should offer more money.
Microsoft first made the offer for Yahoo! in January, but it was rejected as being too low. Since then, Yahoo! is understood to have been in talks with other media companies in the hope of finding a white knight. These have included News Corp, AOL-owner Time Warner and Google, although Rupert Murdoch has ruled out a move, saying "we're not going to get into a fight with Microsoft, which has a lot more money than us".
If Microsoft were to pursue the threat laid out in the letter, it could be a lengthy process that would require the company to get Yahoo! shareholders to boot out existing directors at its annual general meeting. There is no exact date set for the AGM at this point but it is likely to take place in June or July.
The letter, written by Microsoft chief executive Steve Ballmer, says: "The substantial premium reflected in our initial proposal anticipated a friendly transaction with you.
"If we are forced to take an offer directly to your shareholders, that action will have an undesirable impact on the value of your company from our perspective which will be reflected in the terms of the proposal."
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