How can I make a new home base?

Solution 1:

It is possible that you haven't finished the 'Home Away from Home' mission yet, which is why you have no option to transfer to that potential home site. (You'll know when you have finished it when you are left just outside Snyder Trucking Warehouse at west Marshall and with Jacob Ritter no longer following you.)

Transferring to a new home site requires that you finish the 'Home Away from Home' mission given by Jacob Ritter, and 100 influence. Home sites also have different building materials and number of survivors requirements. You have to meet those requirements before you can transfer to a new home site.

There is no need to make a location an outpost before you transfer your home site to it. Make sure you are standing inside a valid home site before making a radio assistance call that you want to transfer your home site to that location.

I am listing here the available home sites you can transfer to and and their requirements (click the links on the name of a home site for more info on them):

Home Site — Materials — Survivors (base game) — Survivors (Breakdown DLC)

• Kirkman Residence – 30 – 8 – 6
• McReady Farmhouse – 30 – 8 – 6
• The Alamo – 20 – 5 – 0
• Savini Residence – 30 – 8 – 6
• Snyder Trucking Warehouse – 50 – 12 – 10
• Trumbull County Fairgrounds – 50 – 12 – 10
• *Church of the Ascension – 20 – 5 – 0

^{*Note: In the base game, transferring to this home site is part of the storyline. While, in the Breakdown DLC, you can opt to make this your home site.
Attribution: Home sites requirements info are from the State of Decay wiki}

Solution 2:

In the mission "Home away from home", Jacob first leads you to the Savini Home Resident, where you witness a dying man reanimating. After that, the map pointer points to another place, the Snyder Trucking Warehouse. Then you get out of the car and have another talk with him, and he repeatedly insist that you choose the first home site you visited. At that point, the mission ends and the option to relocate home base is unlocked.

So, did you do all these and the option is still missing?

P.S: The relocating requirements include Influence, People and Material, nothing more. If you don't fulfill the requirements, the option will be greyed out, not missing. If it's missing then it's likely that you haven't completed the required storyline mission.