Has the Beechcraft company considered building a single-engine turboprop?
Yes.
https://www.google.com/search?q=single+engine+king+air
Top result:
http://www.flyingmag.com/aircraft/beechcraft-reborn

Perhaps the most intriguing product floated by HBC at its NBAA press conference was a single-engine turboprop. The company says the airplane has no public name or designation but will “absolutely,” said Holcombe, be “called a King Air.” That name, of course, has never been bestowed upon a single-engine airplane before.
This King Air, however, will be no scaled-back PT-6 single. Like the remarkably roomy and powerful Pilatus PC-12, the Beechcraft single will be big. Its fuselage will be — get this — based on that of the Premier 1A, which, HBC claims, has the best cabin of any bizjet in its class. It will certainly be huge for a single. In addition to the voluminous cabin, the single would feature a large side loading door, room for eight to 11 occupants and industry-leading pressurization. The composite fuselage allows for efficient pressurization. HBC says it will build the fuselage in the same way it builds the Premier 1A today, using state-of-the-art winding technology for extremely light and strong composite structures.