No, they didn't.
Nazi official party line was that jews deserve their own country.
Which is why the nazi taxpayer paid to resettle jews into israel.
en.wikipedia.org
Furthermore, the entire argument for the gas showers is that nobody knew there was a genocide going on. The inmates thought they were only being imprisoned and not killed. The gas showers were thus a trick to perform secret executions.
This is also why they didn't just shoot them.
They instead spent extreme amount of money and effort to ship them out of the country to auswitz. (note that all camps captured by USA were proven to not be death camps. rather "reeducation through hard labor camps". only death camps found were in areas conquered by USSR).
This was all to maintain the illusion that there is no genocide and they are enlightened people who just want segregation and nothing else.