javascript: is there a vulnerability if users can call any URL from their hosted website?

I am developing a website where a functionality allows users to provide any URL that will then be converted into an ajax request and called. This can happen through GET or POST methods, but only through javascript on the client side. The URL will be requested from the client side only.

What problems can arise due to this? What are some ways this can be viewed as a vulnerability for the web application?

An example Javascript function for what I am trying to do:

sendPostRequest (url, callback) function
{
$ .ajax ({
type: "POST",
url: url,
success: callback
});
}

Here url is obtained from the user's input.