Back-to-back wins have seen Mark Warburton's side climb into fifth place in the table, just two points behind Derby County.
With the latter otherwise occupied in the FA Cup, Brentford can move within two points of leaders Bournemouth if they take all three points at Carrow Road.
Norwich, themselves a point out of the play-off pack, have been very strong at home recently with three consecutive victories and new manager Alex Neil has won his first two games in charge.
Brentford will have Chris Long in their ranks after he completed his loan move from Everton earlier this week, and Warburton hopes he can boost their chances during his spell at Griffin Park.
"We are looking forward to seeing how he [Long] benefits from the loan move and how he impacts the team's performance," he told the club's official website.
"Chris is a young boy with enormous potential and who will add value to the group over the coming weeks."
The Championship's top six could be shaken up this weekend with Watford facing beleaguered Blackpool.
Lee Clark's side remain rooted to the foot of the table after defeat to Wolves last weekend – their 15th defeat of the league season – and they have only taken five points on their travels.
That will provide a boost to Watford, who come into the game off the back of a comprehensive 5-0 destruction of Charlton Athletic and are chasing a victory that would ensure Slavisa Jokanovic's side remain in the top six.
One of the clubs chasing a top-six spot are Wolves, who host Charlton at Molineux looking to add to Guy Luzon's woes.
The Israeli took over at the Valley last week, but was not in the dugout for Saturday's defeat at Watford – their 10th game without a win in all competitions.
At the bottom, Wigan Athletic welcome Huddersfield Town to the DW Stadium and Malky Mackay will be keen to make full use of home advantage.
Wigan currently sit 23rd in the table – four points clear of Blackpool – and a rare victory would see them move within two points from safety.
There is plenty at stake for Huddersfield, though, with three points adding to their eight-point cushion on the bottom three.
