A Stardock employee said the following on the GOG.com forums:
"Atari has the trademark for Star Control (obviously a key component) and the (c) for Star Control 3.
But Paul Reiche owns the (c) for Star Control 1/2. You couldn't do a HD version of Star Control 1/2 without his permission.
In terms of the game universe itself, we wouldn't (I work at Stardock) want to do anything that would be considered "canon" without Paul Reiche's blessing and, ideally, involvement.
None of this will affect Star Control on GOG except where checks get sent to.
Stardock is already a GOG partner.
But there will be a new Star Control game with Star Control 2 serving as a major source of inspiration.
That's about all I can say at this time."