From Dr. Dave Ultimate Prep:

Realistic. Answer what is Alex Trebek over hosting “Jeopardy” much longer.

The game show host was on the latest episode of “OBJECTified” with Harvey Levin and talked about when he’ll likely step down from hosting duties. Trebek believes he’ll mostly likely be done when his contract expires in 2020. But, since he is very much part of the production side of things, will still be active.

As for who he thinks should take the reigns, it’s Alex Faust, the LA Kings hockey announcer. Another option he has in mind is CNN legal analyst Laura Coates. We shall see!
Source: TMZ