Zendesk Inc. ZEN, +1.29% shares soared 35% to $78.36 in after-hours trading Thursday following a report from The Wall Street Journal that the company is close to a deal with a group of buyout firms.

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 Journal said, citing people familiar with the matter. The price in what would be one of the biggest private-equity takeovers of the year couldn’t be learned, the report said.

It is not clear where Zendesk’s discussions with Jana Partners LLC stand in light of the expected buyout deal, the Journal said. The company had been expected to strike a settlement agreement with the activist investor days after the company ended a bid to sell itself in a private-equity action, the Journal reported last week.