Yahoo is due to hold an annual general meeting at the start of August
Software giant Microsoft says it would be willing to re-open talks with Yahoo about a possible takeover if the search firm had a new board of directors.
Microsoft had offered to buy its rival's search business but was rebuffed by Yahoo last month.
A number of investors have criticised Yahoo's decision. Yahoo shares closed up 12% at $23.91.
Microsoft said it could start talks with a newly elected board after Yahoo's August shareholder meeting.
The software giant said in a statement it would be interested in discussing two options - buying the "search function with larger financial guarantees" or "purchasing the whole company".
Shareholder Carl Icahn is trying to oust Yahoo's board, including the internet firm's co-founder and chief executive Jerry Yang.
US billionaire Icahn, who has amassed a 5% stake in Yahoo, has been in talks with Microsoft over the past week about a possible deal.
The corporate raider has said that replacing Yahoo's nine directors at the firm's annual meeting on 1 August is the only way to salvage a deal with Microsoft.
But Yahoo said the push by Microsoft's chief executive Steve Ballmer and Mr Icahn to force it into selling its search business was not in the best interests of shareholders.
"If Microsoft and Mr Ballmer really want to purchase Yahoo, we again invite them to make a proposal immediately," Yahoo said in a statement.
This is Microsoft's clearest message yet that it is willing to strike a fresh deal with Yahoo since takeover attempts collapsed last month.
Microsoft originally offered to buy Yahoo in January - with an offer worth about $47.5bn (£24.1bn).
But Mr Ballmer withdrew that bid in May after Yahoo's boss Jerry Yang demanded a higher price.
The software maker then tried to buy Yahoo's search business for $1bn and pay another $8bn for a stake in its remaining operations.
Yahoo spurned Microsoft, opting for an online advertising partnership with rival Google instead.
That deal is being analysed by US anti-competition officials as the two firms combined would control more than 80% of the US search advertising market.