Despite being advised by the special committee that he should raise his offer to see the transaction through, Michael Dell was non-committal, the person added, confirming an earlier report by Bloomberg News.
Dell and Silver Lake declined to comment.
The special committee's move came as Icahn and his affiliates disclosed on Tuesday they had provided $3.42 billion, or 66 percent, of the debt financing to back his bid for Dell.
Investment bank Jefferies & Co provided $1.6 billion, or 30 percent of the overall $5.2 billion in committed financing with the remainder of about $179 million coming from 14 institutional funds, including pension funds and insurance companies, according to a U.S. Securities and Exchange Commission filing.
"The fact that he could not get lending from other banks suggests they are not too friendly to this," said Steven Kaplan, a University of Chicago finance professor. "However, one must note that a few banks are locked up with the Silver Lake offer."
"On the positive side, Icahn is putting a lot of money where his mouth is," Kaplan added.
Other market participants evaluating the transaction said Icahn's move could indicate he may never have aimed to broadly distribute the deal in the first place.
(Read More: Icahn Proposes Dell Tender, Becomes Second Largest Shareholder)
Calls to Carl Icahn, who runs Icahn Enterprises, were not immediately returned.
Icahn and Southeastern Asset Management are preparing an offer that would see shareholders tender 1.1 billion shares at $14 apiece, rivaling Michael Dell's and Silver Lake's $24.4 billion buyout offer of $13.65 a share.
The billionaire investor has said Michael Dell's offer substantially undervalues the company. Dell's special board committee had recommended Michael Dell's offer to shareholders.
While the financing commitment marks a crucial step forward for Icahn's bid for Dell, it is contingent on a dozen board appointments, according to the SEC filing.
Unless all 12 of the nominees proposed by Icahn and Southeastern on May 13 are elected to Dell's board, the financing is unlikely to take place.
Icahn's proposal will also be put to shareholders only if the offer by Michael Dell and Silver Lake is not accepted by shareholders when they meet on July 18.
'Game of Chicken'