On Twitter, Google’s Gary Illyes said that it was not necessary to change the links to your HTTP pages when you switch your website to HTTPS:
@pip_net if your redirects are properly implemented, the benefit from doing that is so minimal that IMO it's not worth it.— Gary Illyes (@methode) July 7, 2015
In other words, you don’t have to ask the websites that link to your site to change the links from HTTP to HTTPS.
There are many more important things that influence the position of your web pages on Google’s search results. Use the website audit tool in SEOprofiler to find things that have a negative influence on your website’s rankings: