A deal could be announced as soon as this week, the sources said, cautioning that negotiations had not been finalized and that an agreement was not certain.
The sources asked not to be identified because the negotiations are confidential. Salesforce and MuleSoft did not immediately respond to requests for comment.
Shares of MuleSoft jumped more than 20 percent after being briefly halted following the report.
Salesforce invested in MuleSoft when it first went public in March of last year.
The enterprise software company provides a platform to help companies stitch together disparate software applications, data and devices. Customers include The Coca-Cola Co., McDonald's, Netflix, Spotify, Unilever and Barclays.
(This version of the story was refiled to correct day of week in first paragraph.)
— CNBC's Sara Salinas and Anita Balakrishnan contributed to this report.