The Championship side have been searching for a new boss since Michael Appleton left for Blackburn Rovers on Friday.
Houston, who has helped the Tangerines lift the Scottish Cup and qualify for Europe three seasons running since arriving in 2009, is out of contract at the end of the season.
Blackpool turned their attention to the Tannadice boss after a move for Bradford boss Phil Parkinson was blocked.
A Dundee United spokesperson confirmed: "The club have granted Blackpool permission to contact Peter Houston.
"That's on the basis that, as a football club, we won't stand in the way of anyone furthering their career."