Sunderland are still looking for their next manager, having recently parted company with Simon Grayson.
The Black Cats are still looking for their next manager, having parted company with Simon Grayson in the wake of their 3-3 draw with Bolton Wanderers at the Stadium of Light last month - his departure was announced just 17 minutes after the final whistle.
In the early weeks of the season it appeared that the Bees may be joining Sunderland in the relegation battle in the Championship, but they have since put together a nine game unbeaten run in the league, winning four of their last five and dismantling Leeds in their most recent game before the international break.
And Andrews has heaped praise on the job that Smith has done at Griffin Park, suggesting that Sunderland would be making a mistake not considering him for the post.
"I don't see why not [he can't progress]. We're going to talk about Sunderland later and why should he not be in that equation? I think he's done that well, nothing hits the papers, there's no drama around them [Brentford], it's just seamless," he told EFL Matters on Sky Sports.
"He comes in, he works, he gets his team organised. He gets the players buying into it, and the brand of football for me is nigh on spot on."
While Sunderland should have more potential as a club if they can get their act together, it is difficult to see why Smith would actually want to leave Brentford for the Stadium of Light right now.
Grayson was an unpopular man by the time his departure was announced, but the circumstances he had to work in made the job extremely difficult.
Meanwhile, there seems no reason why - based on the way that they are currently playing - Brentford cannot continue their ascent up the table following the international break and start closing that four point gap to the top six.