According to the document which was pointed out by Protocol editor Mike Murphy, users would be able to add external links with their posts on the app, but be charged for the service.
At present it's not possible to have a clickable URL in a caption, but the pop-up message shown in the patent hints this could change in the future.
The message reads: "Would you like to activate the link in your caption for $2?"
However, just because there's a patent for it, that doesn't mean it's going to end up on the app.
Meanwhile, last month, Instagram announced a new Suggested Posts feature in a bid to keep users scrolling.
The new section will appear at the bottom of people's feeds when all of their recent posts by the accounts they follow have been shown.
They will see a message which reads "you're all caught up", before being given suggestions of accounts to browse based on their interests and the kind of posts they interact with.
Robby Stein, Instagram's consumer products lead, told CNN: "It's like an extension of your feed."
It's a similar tool to the Explore page, however, Suggested Posts is more specific.
Instagram has said they have created Suggested Posts to make it "easier to go a little deeper".
They said in a statement: "We see people continuing to seek out more posts they're interested in after catching up with their feeds, so we wanted to learn from that and make it easier to go a little deeper for those who choose to do so."