Cisco Systems Inc. has made a takeover offer worth more than $20 billion for software maker Splunk Inc., according to people familiar with the matter.

The offer was made recently and the companies aren’t currently in active talks, some of the people said.

Should there be a deal, it would be Cisco’s biggest ever, eclipsing the roughly $7 billion...

Cisco Systems Inc. has made a takeover offer worth more than $20 billion for software maker Splunk Inc., according to people familiar with the matter.

The offer was made recently and the companies aren’t currently in active talks, some of the people said.

Should there be a deal, it would be Cisco’s biggest ever, eclipsing the roughly $7 billion acquisition of Scientific Atlanta in 2005. Its most recent deal of size was its nearly $5 billion purchase of Acacia Communications Inc. in 2021.

Splunk is currently searching for a chief executive after Doug Merritt stepped down from the role in November after roughly six years following a series of disappointing earnings reports. The company named Chairman Graham Smith as interim CEO, a position he still holds.

Splunk shares rose sharply early in the pandemic as did those of a number of other technology companies with strong growth potential, but have almost fallen in half since then.

It isn’t clear whether other potential suitors are circling Splunk.

Splunk, founded in 2003, makes software used by companies’ information-technology and security operations to monitor and analyze data.

San Jose, Calif.-based Cisco sells routers, switches and security services as well as software products such as its Webex meeting application.

Cisco’s interest shows that the networking giant—a serial acquirer, but usually of smaller companies—has an appetite for big deals.

And it has the wherewithal, with a market value of around $235 billion and more than $20 billion in cash and short-term investments.

Software has been a hot corner of the M&A market lately, with a number of companies in the sector being snapped up by private-equity firms or other industry players. In one of the latest examples, Citrix Systems Inc. agreed to be taken private by a pair of private-equity firms in an acquisition valued at $16.5 billion, including debt.

Splunk said in June that technology-focused private-equity firm Silver Lake was making a $1 billion investment in the company to help support the transformation of the business. Splunk has been shifting from a traditional software-licensing arrangement to a cloud-based subscription model. An increase in the shares on news of that investment had evaporated by the close of trading Friday.

Cisco is set to report its fiscal second-quarter earnings Feb. 16, while Splunk reports March 2.

Write to Dana Cimilluca at dana.cimilluca@wsj.com and Cara Lombardo at cara.lombardo@wsj.com