Blackstone Group LP (BX) is open to keeping Dell Inc. (DELL) founder Michael Dell as chief executive under its plan to gain control of the computer maker, people familiar with the matter said.

The private-equity firm is competing against an offer from Mr. Dell and private-equity firm Silver Lake Partners to take the company private.

Hedge-fund investor Carl Icahn also made a proposal for Dell late last week, and a special committee of Dell shareholders is reviewing the offers.

The fate of Mr. Dell could be a deciding factor in the outcome of the battle for the company. He started Dell, still runs the company and is its largest shareholder.

Openness by Blackstone to keeping Mr. Dell might help the private-equity firm sway the CEO to eventually side with its bid.

While Mr. Dell ignited the takeover battle by joining forces with Silver Lake to offer $24.4 billion to take Dell private, he has agreed to consider all competing proposals.

Blackstone also values Mr. Dell's strategic importance in the company's management, seeing him as an important potential ally if the Blackstone-led bid prevails, according to a person familiar with the matter.

Is isn't clear if Mr. Dell is aware of Blackstone's position or would be interested in remaining CEO if Blackstone's bid succeeds.

Blackstone also has approached other executives about potentially taking over, people familiar with the matter have said. Mr. Dell was unhappy when he found out about those efforts, a person familiar with his thinking said.

Mr. Dell also opposes a Blackstone proposal that might result in the sale of the Dell finance unit that provides loans to customers to buy its products, the person said.

Terms of the takeover offer by Mr. Dell and Silver Lake include $13.65 a share for Dell. Blackstone offered at least $14.25 a share, while allowing shareholders to retain some of their stock.

Write to Matt Wirz at matthieu.wirz@wsj.com and Sharon Terlep at sharon.terlep@wsj.com

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