The agreement, in exchange for a modification to rules for voting on the deal, would include a special dividend of 13 cents per share along with an increased offer of $13.75 per share, said the source, who spoke on condition of anonymity.
Dell shares were up about 4 percent at $13.47 before the bell.
Any new pact would probably delay the process for a vote by Dell shareholders by about another month, the Wall Street Journal reported earlier.
Dell could not immediately be reached for comment. Its buyout partner, Silver Lake, declined to comment.
Dell shareholders are scheduled to convene for a third time on Friday to vote on Michael Dell's $24.4 billion buyout proposal, helping to decide the fate of the No. 3 PC maker after months of dueling with Carl Icahn and other unhappy investors.
The meeting in Round Rock, Texas, comes after two previous adjournments, when the company was not certain of gaining enough votes for what would be the biggest buyout since the financial crisis.
The voting-rule change would count only shares that are actually voted. An earlier clause had abstentions counting as "no" votes.
Unless it is postponed again, Friday's vote may prove crucial in determining the future of the struggling company. Its founder and private equity firm Silver Lake want to buy and take the company private, arguing that a painful restructuring can best be performed away from Wall Street's scrutiny.
But the battle over that deal, announced in February, has raged for months, casting a pall of uncertainty over a company already shrinking along with a rapidly declining PC market.
The CEO, his advisers and proxy solicitors have gone back and forth with shareholders whose votes are needed to secure the deal. They've had some success, managing to get prominent investors such as BlackRock Inc and Vanguard onboard.
But activist investor Icahn, who views Michael Dell's offer of $13.65 as too low, has amassed an 8.7 percent stake in the company and is leading an opposing charge with Southeastern Asset Management, with an offer of his own.
The Michael Dell-Silver Lake group said last week it would raise the offer to $13.75 per share if the voting rule was changed.
Icahn has campaigned hard to get Dell to set a date for an annual shareholder meeting so he can put up his own slate of directors for the company.
On Thursday, he fired his latest broadside, suing Dell Inc and its board to try to block substantial changes to the CEO's buyout offer that may affect the outcome of any shareholder vote and force the company to set a date for an annual meeting.
Dell shares are expected to fall sharply if the deal falls through. On Thursday, they closed just below $13.
Round and round
Sources say the outcome of any vote remains a toss-up unless the deal's terms are changed by the company's special committee, appointed to review the deal.
Abstentions currently count as "no" votes, and with an estimated quarter of eligible shares not having voted either way so far, that is a substantial hurdle to overcome.
The special committee, however, rejected that requirement after several major shareholders expressed outrage. Instead, the committee offered to change the record date, or the date at which a shareholder is considered eligible to vote.
Such a change is also considered beneficial to getting the deal pushed through, because a later record date would bring a lot of so-called arbitrage investors into the game, who are deemed more likely to want a deal.
In the longer term, investors remain divided over Dell's prospects. Some are ready to cash out of a company increasingly vulnerable to a crumbling PC market.
The company created by Dell in his dorm room in 1984, and which rapidly grew into a global market leader renowned for innovation, is now a shadow of its former self.
Others, led by Icahn and Southeastern Asset Management, are convinced the company still has time to transform itself into a dominant provider of business computing services.
Icahn has accused the company of resorting to "scare tactics" by disclosing bad news and dismal forecasts. Dell reported a 79 percent drop in profit in its latest quarterly report.
(Also see: Dell takeover battle: All you need to know)
© Thomson Reuters 2013
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