The source said the offer was increased "by several dollars," The New York Times reported.

Some Yahoo! shareholders have received calls from both companies asking what size of a purchase offer they would accept.

Microsoft Corp. Chief Executive Steven Ballmer told employees earlier this week that the company could negotiate, get tough or walk away from pursuing Yahoo! Inc., sources said.

Yahoo! has rejected Microsoft's purchase offer of $31 per share, but Chief Executive Jerry Yang had said Yahoo! would consider a larger offer.

With stock values shifting since the initial offer was made, the price had gone down to $29.30 per share.

Some shareholders said they were waiting for the offer to reach $35 a share but one said he believed the deal could be settled at $34 a share, the Times reported.

Ballmer told Microsoft employees earlier this week, "I know exactly what I think Yahoo! is worth to me. I won't go a dime above and I will go to what I think it's worth if that gets the deal done."