While it's indeed hard to get objective measurements looking at the codebase alone, telling a manager things like
"look, this is going to take 5x the amount of time it should because the current code is a complete mess so I have to be extra careful not to break things and it takes way longer than it should to figure out where I have to put the new feature in order to mimimize the amount of extra chaos created"
or
"I cannot do anything sensibly without refactoring this first but it will pay off in the next couple of months and years to follow"
should make it pretty clear the quality isn't where it should be. If management doesn't grasp that, or doesn't want to hear it, then management quality is probably at the same level as the code's. I know I'm in a position not every developer is, but when needed I ask and get extra time for things like this. Because I've seen what happens when you try to build a trainwreck on top of existing ones: that stuff is exponential, at least.