The phrase suggests a vague, soon-ish future without specifying exact timelines. The construction work is expected to complete in the not too distant future.
Pro Tip 2/3
Promise of Change
Implies that something different or new will happen relatively soon. You'll be hearing from us in the not too distant future with exciting news.
Pro Tip 3/3
Anticipation Creation
The phrase creates a sense of anticipation or expectation for what's coming. The findings of the study will be published in the not too distant future.