So far I know Currently, there is no method available in RestAPI provided by Microsoft available here
There is an alternative to generate report by utilizing Url Access (SSRS)
URL access to the report server in SQL Server Reporting Services (SSRS) enables you to send commands to a report server through a URL request.
URL Access Syntax
URL requests can contain multiple parameters that are listed in any order. Parameters are separated by an ampersand (&) and name/value pairs are separated by an equal sign (=).
Export a Report Using URL Access
You can optionally specify the format in which to render a report by using the rs:Format URL parameter. The HTML4.0 and HTM5 formats (rendering extension) will render in the browser and for other formats, the browser will prompt to save the report output to a local file.
For example, to get a PDF copy of a report directly from a native mode report server:
http://myrshost/ReportServer?/myreport&rs:Format=PDF
You can also provide parameters to this using syntax
http://myrshost/ReportServer?/activeusers&UserStatus=true&rs:Format=PDF
For more details, you can visit
https://docs.microsoft.com/en-us/sql/reporting-services/export-a-report-using-url-access