Zendesk Inc. is close to a deal with a group of buyout firms, according to people familiar with the matter, resurrecting a failed attempt to sell itself in what would be one of the biggest private-equity takeovers of the year.

A deal with a group that includes Hellman & Friedman LLC and Permira could be struck in the coming days assuming the talks don’t fall apart, the people said. The price couldn’t be learned.