Adding 'seams' into the monolith (and exposing this typically via REST or AMQP) is the most effective way I have found.

The alternative is to 'screen scrape' the data returned from calling the monolithic application via the interface exposed now. For example, calling a website page, parsing the HTML data returned, and extracting what you require. However, the code/algorithms you have to write are typically complicated, and the resultant code often fragile and highly-coupled