With Swansea sitting 15th and having won just one of their first five games, former Manchester United midfielder Giggs is reportedly top of the Welsh club's list of replacements.
But the 42-year-old has had no contact from the club - although he did admit he still wants to pursue a coaching role.
“There has been no approach from Swansea City but, in any case, there is a manager in place at the club," Giggs told talkSPORT.
“I'm happy with life outside of the game right now and enjoying media work.
“At some stage, further down the line, it's no secret I'd like to get back into football as a coach – but that's for later, not now."