A private equity group consisting of Bain Capital LLC and Golden Gate Capital is the favourite to reach a deal to buy systems management software vendor BMC Software.
The group is said to have outbid a syndicate made up of KKR & Co LP, TPG Capital LP and Thoma Bravo LLC, sources told Reuters.
Although the exact bids from the consortium and private equity group could not be found, a source said the offers came in a range of $45 to $50 per share, valuing BMC at more than $6.5bn (£4.18bn).
The sources, who asked to remain anonymous as the matter is not public, said that the rival syndicate could still raise its bid or BMC could decide to opt out of selling, with a final decision likely to come in the next week.
The company was forced to put itself up for sale following the intervention of "activist" hedge fund Elliott Management, which also played a key part in forcing BMC rival Compuware to put itself up for sale.
Elliot had attacked BMC's management at the end of 2012, arguing that it had been slow to recognise the opportunity of the internet and software-as-a-service (SaaS) like some of its rivals, notably ServiceNow - BMC admitted the charge.
The firm competes with the likes of Oracle, SAP, CA and Compuware, but unlike many of those firms BMC has not yet invested heavily in the SaaS market.
A 30 January regulatory filing states that Elliott owned about 9.6 per cent of BMC, and he called for the board to be replaced so that the company could be revived with "fresh thinking".
BMC's immediate response was to launch a $1bn (£660m) share buyback.
Elliott had also called on the firm to trim its headcount, a step that it took last month when it said a restructuring programme will result in a pre-tax charge estimated at between $33m and $38m (£21m and £25m). The firm did not disclose the number of employees affected.
The company's shares ended trading at $45.58 yesterday, giving it an overall value of $6.5bn (£4.18bn).
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