The private equity group which owns compliance and energy services group Sureserve is among the bidders circling a division of NCC Group, the London-listed cybersecurity company.
Sky News understands that Cap10 has expressed an interest in buying Escode, which specialises in software escrow and verification services.
City sources said that Platinum Equity, a US-based buyout firm, was also among Escode's suitors.
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Interest from earlier bidders, including Bridgepoint and Montagu Private Equity, is said to have waned.
A deal could cost any buyer in the region of £300m.
Last week, Sky News revealed that NCC Group had kicked off a strategic review of its main cybersecurity operations which could also lead to a sale.
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The Escode process is being handled by bankers at Lazard, with the cybersecurity division's review overseen by Rothschild.
NCC has confirmed both sets of discussions to investors, although their outcome remains unclear.
The group employs about 2,200 people across Europe, North America and Asia-Pacific.
Shares in NCC Group were trading on Wednesday morning at about 146.8p, giving the company a market valuation of roughly £467m.
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Cap10 and NCC declined to comment, while Platinum could not be reached for comment.