The solution depends entirely on your Analytics implementation.
So, ignoring Target entirely (i.e. pretend that you don't have it running on your website), currently, when a user clicks that link that you want the URL for, is there any Custom Link tracking on that link click?
The easiest way to check would be with the AEP Debugger browser extension. This extension assists you to check all of the Adobe-related network requests originating from your browser activity. In that extension, click "Analytics" in the left rail. As you browse your website, the extension's view will fill up with columns of data, where each column represents a network request going to Adobe Analytics arising from a tracking implementation. The most common one that you'll see are for Page Views. But if Custom Link tracking has been implemented, then you'll also see columns of data for Custom Links. (There's a row called "Is Page View" that lets you identify the columns that are for page views vs not page views.)
Back to your situation. When you click that link that you want the URL for, do you see a corresponding column in the Debugger's "Analytics" view? If so, then do you see any eVar or prop row in that column that contains the link's URL? If the answers to both are "yes", then yes, you can indeed run a report showing the URL and its clicks within Analysis Workspace.
Hope that helps.