So you're the new guy that's been assigned to this project...possibly at the request of the current developer who desperately needs help...possibly because it's the project that existing staff don't want to work on...possibly to learn the project so the current developer can be moved to other projects. Every software company has these projects and many developers have been in your position. As long as the software is…
Rewrites are riskier when requirements need to be reverse engineered from the current solution, or if requirements are complex. When requirements are simple, rewriting should be simple. This should at least give you the opportunity to contain technical debt to the most complex requirements. To say "everything is complex therefore we cannot rewrite anything" is pretty implausible and mediocre.
"The idea that new code is better than old is patently absurd. Old code has been used. It has been tested. Lots of bugs have been found, and they’ve been fixed. There’s nothing wrong with it." - Joel Spolsky