I've answered a similar question here before so this might be considered a duplicate. Basically, you're not going to get signoff to do a "refactoring effort". The way you make the code cleaner is to follow the boy scout rule: always leave code cleaner when you leave it than when you arrived.
Just like paying down real debt can seem like an insurmountable task (or cleaning up a messy house). The trick is to make it better piece by piece until you start seeing "islands of cleanliness". Once you have significant momentum, other developers on the team will start noticing and eventually contributing to the task.
I'd suggest reading the Clean Coder by "Uncle" Bob Martin. Writing good code is part of your job. You don't ask permission to do your job, you just do it.