Icahn has reportedly bought about 50m shares, or 3.6% of , in the 10 days since Microsoft withdrew its $47.5bn (£24.5bn) takeover offer.
He has until tomorrow to decide whether or not to nominate any replacement directors for a shareholder vote at Yahoo!'s annual general meeting on July 3. This would give him six weeks to convince other investors to lobby for change.
Icahn has support from fellow Yahoo! shareholder and activist Eric Jackson, president of hedge fund Ironfire Capital.
Jackson has also been working to nominate candidates for Yahoo!'s board, alongside a group of 150 individual shareholders who own about 3.3m shares combined. He has been critical of Yahoo! CEO Jerry Yang's failure to secure a deal with Microsoft.
Jackson said he would support nominations from Icahn as long as "they are strong candidates and don't support selling to Microsoft at too low a price."
However, it is unclear whether Microsoft would agree to reopen negotiations with Yahoo! even if Icahn was successful in convincing Yahoo! to reconsider.
The software giant originally bid $31 and then raised its bid to $33 a share, but it was not enough to secure a deal. Yahoo! had been looking for $37 -- a price that Microsoft was not prepared to meet.