The dropdown doesn't seem to have Greatsword under the melee weapon dropdown

Each of these weapons can be any simple or martial weapon that lacks the heavy and special properties. The longbow is also a valid choice.

The greatsword has the heavy property, and thus is not an eligible choice for Kensei.

Kensei weapons:

"Each of these weapons can be any simple or martial weapon that lacks the heavy and special properties."

Greatsword has the Heavy property and so cannot be chosen.

Edit: Sniped. ; )

Ah makes sense. I think I was thrown off by seeing greatclub under that list and assumed it was also a heavy weapon :p