As we all know, some links are better than others, some are even worth spending 5+ hours before making the request.
But if your time budget is tight, I would suggest the following, which is done in 5-10 minutes and still adds some (minimal) value to the other party:
- identify the link prospect,
- install Xenu Link Sleuth, run it on the target's website and hope for some errors,
- write your outreach email, include the errors you've found, and if possible a potential solution.
Something like
"I was browsing your website and encountered a [interesting error] which might be because [possible reason why].
By the way, would you be interested in [your offer]?".
Obviously adapt this with acitrano's answer.