Is Jimmy Fallon next in line to host The Tonight Show?

In my opinion, it's only fair that Jimmy Fallon becomes the next host
of The Tonight Show after Jay Leno retires. I think Jimmy is very
funny  i think he is doing a very good job hosting Late Night. I know
Conan O'Brien hosted Late Night for 16 years before he finally got his
turn to host The Tonight Show, and I'm pretty sure Jimmy won't have
nearly as much experience as Conan did when Jay retires, because
obviously Jay's retirement can't be that far away seeing as how he is
61.
I want to know any information regarding this subject.