Cloud-computing company Citrix Systems Inc. is close to a deal to be taken private, continuing a spate of big leveraged buyouts.

Elliott Management Corp.’s private-equity arm, Evergreen Coast Capital, and Vista Equity Partners are near an agreement to pay $104 a share, or roughly $13 billion, for the software company, according to people familiar with the matter.

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Cloud-computing company Citrix Systems Inc. is close to a deal to be taken private, continuing a spate of big leveraged buyouts.

Elliott Management Corp.’s private-equity arm, Evergreen Coast Capital, and Vista Equity Partners are near an agreement to pay $104 a share, or roughly $13 billion, for the software company, according to people familiar with the matter.

The deal could be announced Monday, the people said.

A deal isn’t guaranteed as the talks could still fall apart or the announcement could be delayed.

Should it go forward, the takeover would be the biggest leveraged buyout in recent months, ending the lull that followed a flurry of them in 2021. With interest rates at historic lows, private-equity firms have amassed billions of dollars of cash from investors that they must put to work to begin earning fees on it.

Citrix makes software that allows users to virtually access desktops as well as other cloud-computing capabilities.

Its shares closed Friday at around $105.55, having already jumped on speculation of a deal over the past few months. Bloomberg reported Jan. 14 that Elliott and Vista were in advanced talks to buy Citrix.

Citrix, like many legacy software companies, has had a rocky transition to a subscription-based model for its core virtual-desktop services.

Citrix’s David Henshall in October stepped down as president and chief executive and also left as a director along with another board member, a move that reduced the board’s size to eight members. The company tapped chairman Bob Calderoni as interim CEO.

Citrix has benefited as the pandemic stokes demand for remote-work services, a trend that appears poised to continue.

Still, Citrix’s modest size compared with that of peers such as VMware Inc. and spotty results over the years have made it the subject of takeover speculation. Indeed, it has drawn the attention of private-equity firms and industry players in the past, though no deal was struck.

Elliott has a long history with Citrix. It holds a more than 10% stake worth over $1 billion and had been pushing it to take steps to boost its share price, The Wall Street Journal reported in September.

Elliott has gone on to buy other companies it agitated at, including health-data company Athenahealth Inc., which it agreed to sell last year.

The investment firm took a stake in Citrix in 2015 and held a seat on its board until last spring.

Elliott, while best-known for its activist investments, has been expanding its private-equity practice. Outside of Evergreen, which focuses on technology investments and is also an owner of software company LogMeIn Inc., Elliott owns other companies including bookseller Barnes & Noble Inc.

Based in Austin, Texas, Vista is a pioneer in software investing and manages more than $86 billion in assets. Its chief executive, Robert Smith, founded Vista in 2000.

Citrix is expected to be combined with Tibco, a software company Vista already owns, some of the people said.

—Miriam Gottfried contributed to this article.

Write to Cara Lombardo at cara.lombardo@wsj.com