Almost bought a house with one of these. After talking with some people from the town, they had a permanent easement for the line, and it restricted any future expansion due to its proximity to the home. I walked away because I was worried about resale. Remember that everything that we as investors hear as a potential problem, home-owners hear as a MAJOR red flag! Keep looking
What's the story with the pipe? Knowing that will likely get you better answers. How large? How deep? Is it public or private? What is the effect to not only your property's drainage, but all the drainage upstream coming into the pipe? What kind and how many structures (inlets, cleanouts, catch basins ect)?
Is this a city storm sewer? Sanitary sewer? If its city owned, you almost certainly cannot just move it yourself. There might be a process where you could get it done, at your expense. This can be very expensive. We have drainage issues around here, and I have personally discussed storm sewers with the public works director. A new drain along the edge of my property, leading to the creek nearby would be ideal. He agrees. He says is about a million dollars for this line, which would run about four blocks.
Its not as easy as just shifting it over. The slopes must be maintained. More slope often means more digging and more cost. So these lines are typically built at the minimum workable slope. If you lengthen the line in one spot, you will decrease the slope on the section you move unless you also lower the ENTIRE line downstream of where you did your work.