Some of Dell Inc.'s (DELL) biggest institutional shareholders are expected to vote against a proposed buyout of the computer maker, people familiar with the matter said, a blow for deal proponents who felt that this group of investors would likely favor a deal.

Vanguard Group, State Street Corp. (STT) and BlackRock Inc. (BLK), which collectively hold nearly an 11.4% stake in the computer maker as of the latest public filings have signaled they will oppose the deal, one of the people said. Representatives of Vanguard and State Street declined to comment, and a representative of BlackRock didn't immediately respond to a request for comment.

That opposition would bring the count of known planned negative votes to close to 30% of Dell shareholders.

The takeover agreement requires the majority of shareholders outside of Michael Dell and his affiliates, who hold a combined approximately 16% of the shares, to vote for the deal. That means shareholders with just over 42% of shares need to vote yes for the deal to pass.

Dell founder Michael Dell and private-equity firm Silver Lake Partners struck a deal to take Dell private for $13.65 a share. A vote on the deal is scheduled for Thursday but will likely be delayed to give the buyout group and company more time to convince shareholders to vote for the deal, people familiar with discussions said Wednesday, although they cautioned that no decision had been made.

--Shira Ovide contributed to this article.

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