The Clarets have regained their form with back-to-back wins in the top flight, while Norwich remain in serious trouble at the foot of the table as focus turns to the domestic cup.
Burnley had been accused of sleepwalking their way towards a relegation fight when losing four games on the spin over the Christmas and New Year period, but they have since arrested that alarming slide with successive wins.
That could well prove to be the turning point in their season, having followed up those three points with another big win away at Manchester United in midweek - their first victory at Old Trafford in 57 years.
There is now a seven-point buffer between Burnley in 13th and Bournemouth in the final relegation spot, meaning Dyche may well take the FA Cup a little more seriously.
The Clarets made eight alterations to their starting lineup for the third-round win at home to Peterborough United but, given the winnable nature of Saturday's tie, changes could be kept to a premium in order to keep momentum building.
This weekend's clash will mark just the second time the sides have met in the FA Cup, with Norwich winning 4-1 the only other time they faced off in a third-round tie eight years ago.
The Canaries finished 12th in the Premier League that season, though it is fair to say that their ambitions are a little lower this campaign with time running out to save themselves from relegation.
Daniel Farke's men temporarily revived their survival hopes with a 1-0 win over Bournemouth last weekend, only to concede late on in a 2-1 loss at Tottenham Hotspur on Wednesday, leaving them six points from safety.
Norwich will therefore have bigger things on their mind than a cup run, even if there is a seven-day break before their next Premier League outing, a trip to Newcastle United on February 1.
Taking all competitions into account, the Canaries have won just one of their 21 away visits to Burnley - a 4-1 victory in April 2004 - with 16 of those matches ending in defeat.
With just five wins from 26 games all season, hope will not be high of improving on that disappointing Turf Moor return this weekend.
Burnley's FA Cup form: W
Burnley's form (all competitions): LLWLWW
Norwich City's FA Cup form: W
Norwich City's form (all competitions): DDWLWL
If Dyche elects to field a strong XI and starts Jay Rodriguez in attack, the 30-year-old will be looking to build on a return of nine goals in his last 13 FA Cup appearances, including a goal in each of his last three outings for Burnley in the competition.
Top scorer Teemu Pukki has scored in back-to-back matches, ending a previous run of four games without a goal, but will surely be rested here.
Onel Hernandez was also on target at Deepdale and is expected to start here following a string of substitute appearances in the league.
Burnley possible starting lineup:
Hart; Lowton, Tarkowski, Long, Pieters; Hendrick, Westwood, Cork, McNeil; Wood, Rodriguez
Norwich City possible starting lineup:
McGovern; Byram, Zimmermann, Amadou, Lewis; Tettey, McLean; Cantwell, Stiepermann, Hernandez; Idah
We say: Burnley 3-1 Norwich City
Burnley have lost only two of their last 20 home FA Cup games - 2-0 to Arsenal in January 2008 and 1-0 to Lincoln City in February 2017 - and we expect them to get the job done against Premier League strugglers Norwich on Saturday.