No. Instagram does not send a notification if you reject someone’s follow request. However, they may figure it out if they visit your profile after you have rejected it.
When someone requests to follow you, a white button will appear underneath your profile. This button will say “Requested”. In other words, the app is telling you that you have already requested to follow this person.
This will white button will remain on that person’s Instagram profile until they decide to Accept or Reject your request. This is because follow requests on Instagram do not expire.
How to tell if someone rejected your follow request on Instagram.
If you return to the person’s page and see that the white “Requested” button is no longer there, then it means that they have rejected your follow request.
If this is the case, then the “Requested” button will change back into the blue “Follow” button.
Essentially, this means that there are ways to for someone to figure out whether you rejected their request or not. However, this will depend on how perceptive they are. If they do not return to your profile, then they will never find out.
As I mentioned above, no notification is sent. As a result, they will need to manually revisit your profile in order to check.
Don’t accept or reject it.
To avoid a situation where the other person may find out, you can simply leave the request as it is. In other words, ignore it. Do not press Accept or Reject. This way, the white “Requested” button will remain underneath your profile.
This will give you a plausible explanation if they ever broach the subject. i.e. You can say that you haven’t been using Instagram or that you simply did not see their request for some reason or another.
Similar articles that you might find helpful.