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Quest in March had agreed to be acquired by investment firm Insight Venture Partners for $23 a share, or about $2 billion, and then earlier this month disclosed that it had received multiple alternative bids.
Based in Aliso Viejo, California, Quest makes software that helps companies manage databases and servers.
Dell has continued to buy up enterprise IT companies in an attempt to reduce its dependence on the slow growing, low margin PC business.
Quest shares in pre-market trading are up 87 cents, or 3.5%, to $26.05.