So, it looks like the idea to relocate city government that pops up every decade seems to have popped back up. The LSJ is reporting
that the city isn't really interested in upgrading the existing location, and see the location as valuable property for commercial development. City government would remain downtown and they are looking at options. From the sound of it it sounds like they are looking at using an existing building or a new construction. The city says that the relocation becomes much more feasible if a combined city-council "justice center" currently being studied is agreed to, which would include Lansing city government and district court, the Lansing Police Department, and the Ingham County Sheriffs Department.
They aren't revealing much, so what is your guy's guess? To my ear, the latter proposal for a combined city-county building sounds like it would probably require a new building. If only the city government is relocated, I'm guessing they could put it in the Temple Building down the street. I can't really think of any other existing space downtown large enough to handle even just the city government alone, let alone a combined city-county justice center. That much office space unless they put it on one of the large state parking lots would require a significantly tall building, taller than what the current city hall is, probably.