The Welsh outfit secured a creditable point in a 2-2 draw at the Emirates Stadium against Arsenal on Wednesday but looked to be denied a priceless winner when referee Lee Probert blew for time while Jonathan De Guzman was breaking through on goal.
The feeling of dropping two points rather than gaining one was a bitter pill for Swansea who are bottom of the Premier League current form table with three draws and three losses from their last six.
Swansea (7-9-15) manager Garry Monk says his side can't dwell on what might have been as they look to secure the win that would allow them to leapfrog Norwich into 14th place.
"We need to use the Arsenal game as momentum going into this match and try to draw on the experience," Monk told the Swansea official club website. "It was a confidence boost against a top side. Those are the sort of performances we need to produce for the remainder of the season.
"Obviously it will be a totally different game on Saturday. We are expecting a tough test. I think their league position belies how good they are because they have some very good players. But we have a good group, and I think you can see by the performances that they all want to do it."
Norwich City (8-8-15) need to improve a wretched away record and fast if they are to maintain their Premier League status.
Only Cardiff City have secured fewer points away from home than Norwich this season, who have just two road wins all season and are winless in seven away league matches.
The Canaries secured a valuable 2-0 home win against Sunderland last weekend through goals from Robert Snodgrass and Alex Tettey.
Manager Chris Hughton will look for his side to build impetus from that result as they seek to secure their first points away from Carrow Road since drawing 1-1 with Crystal Palace on New Year's Day.
"There's always a little bit of a better feel the week after a good result, but we need to make sure we take that feel into the next game and every game we play," Hughton told his club's official club website. "You look for every psychological boost that you can.
"The biggest one for us, of course, is that we're on the back of a good win and performance on Saturday, but we have fared well against Swansea in the last couple of years and hopefully we can use that."
The Canaries boast an unbeaten Premier League record against Swansea winning three times, including the last two at the Liberty, and drawing twice since the sides secured promotion from the Championship in 2011.
Norwich won the corresponding fixture last season 4-3. The Canaries raced to a 3-0 lead through strikes from Steven Whittaker, Sebastien Bassong and Grant Holt. Michu and de Guzman responded for Swansea before Snodgrass sealed the points. Michu struck again deep into stoppage time for a late consolation.
This season's reverse fixture ended 1-1 at Carrow Road. Nathan Dyer fired the Swans in front but Gary Hooper responded for the Canaries.
Norwich will again have to do without Leroy Fer, Michael Turner (both hamstring) and Elliott Bennett (knee).The Swans will be without defender Kyle Bartley (hamstring) but otherwise have a full squad to choose from.