Last week billionaire investor Carl Icahn tried to oust Yahoo's board
Microsoft has said it is considering a deal with Yahoo which would not involve a full buyout of the company.
Microsoft's previous offer to buy Yahoo for $33 a share - a figure which valued the company at $47.5bn (£24.36bn) - was turned down.
Last week Yahoo rebuffed billionaire investor Carl Icahn's plan to oust the current board over the failed merger.
Now Microsoft says it is discussing with Yahoo an alternative transaction, but did not provide any detail.
In a statement, Microsoft said it "is not proposing to make a new bid to acquire all of Yahoo at this time, but reserves the right to reconsider that alternative".
It issued the statement, it said, "in light of developments" since the company withdrew its bid two weeks ago.
Microsoft stressed that a deal may or may not follow from Sunday's statement.
After Microsoft's statement, Yahoo confirmed it was looking at a number of "value maximising" alternatives with Microsoft, and would assess offers made by the firm.
The internet firm said its board would evaluate each of the alternatives "including any Microsoft proposal... with a focus on maximising stockholder value".
Analysts say any agreement could save Yahoo from having to fight a battle with Mr Icahn, who is amassing a stake in the company in an attempt to force out the current board.
Mr Icahn's manoeuvre on Thursday followed much criticism over Yahoo's decision, led by co-founder and chief executive Jerry Yang, to turn down Microsoft's offer earlier this month to buy the company.
Yahoo had wanted Microsoft to increase its bid of $33 a share to $37.
Yahoo has also been looking into an alliance with internet giant Google, and the firms recently tested an advertising partnership for two weeks.
If they were joined together this would make Yahoo a less likely target for acquisition, analysts say.