Although executives have resisted the idea out of fear it would corrupt the app's personal nature, it could help revamp the main feed after it has been eclipsed by stories.
As reported by The Verge, the feature is known internally as "seamless sharing" and it would introduce a new "share to feed" option into the menu at the top-right corner of every post.
Re-shared posts will appear in the feed underneath the photo and username of the user who shared it, and currently posts can be shared twice.
Instagram's co-founders Kevin Systrom and Mike Krieger have fought against the idea of 'regramming' for a long time.
Systrom said last year: "We debate the re-share thing a lot. Because obviously people love the idea of re-sharing content that they find. Instagram is full of awesome stuff.
"In fact, one of the main ways people communicate over Instagram Direct now is actually they share content that they find on Instagram. So that's been a debate over and over again.
"But really that decision is about keeping your feed focused on the people you know rather than the people you know finding other stuff for you to see. And I think that is more of a testament of our focus on authenticity and on the connections you actually have than about anything else."