Bostock and Yang added that any transaction "must be at a value that fully reflects the value of Yahoo, including any strategic benefits to Microsoft, and on terms that provide certainty to our stockholders".
Microsoft made an offer for Yahoo on Febuary 1, for $44.6 billion, or $31 per share.
However a fall in Microsoft's stock price means the proposal now values Yahoo at only $29.62 per share, or just under $41 billion.
In addition, Ballmer said in his letter on Saturday outlining the deadline that the US economic slowdown and volatile stock market had impacted Yahoo's value and there were indications that its search and page view shares have fallen.
If successful, the merger would be the largest in software history and would also provide a serious rival to search giant Google.
Since rejecting Microsoft's bid Yahoo has explored possible alliances with Google, News Corporation's MySpace and Time Warner's AOL, however no viable alternative appears to have emerged so far.