I have a green card. My employer want to move me from US to Canada permanently. Does this jeopardize my US permanent residency?

You can be deemed to have abandoned your lawful permanent residence. Travel to the United States every few months does insulate you from a finding that you have abandoned your status especially considering you will be working and living in Canada. There are options you can explore to preserve your residence. You would be best advised to consult an experienced immigration attorney prior to accepting the transfer.

No, it does not, if you file for and obtain a "Reentry Permit" prior to leaving to work in Canada AND you maintain a home and other ties to the USA, as well as return to the US every few months or so. Consult with an experienced immigration lawyer to efficiently plan this.

If you become a US Citizen this all becoms moot. You can live in Canada however long you want when you become a US citizen.