The wide men both suffered hamstring problems in the goal-less FA Cup third round tie at Sunderland on Saturday.
And while neither injury is considered serious, both are expected to miss out against the Saints.
But boss Sean Dyche is likely to have Jon Flanagan (knee), George Boyd (tendonitis) and Patrick Bamford (sickness) available after missing the trip to the Stadium of Light.
Dyche said: “Johann and Scott are both simplistic hamstring injuries, but I think both will be in doubt, though it’s not impossible they will be available.”
The pair were being assessed further after training yesterdat, after the time of going to press.
Flanagan has missed the last three games with a bruised knee, while Boyd was not risked at Sunderland, and Dyche explained: “Flanno has trained all week and had no reaction, so we’re expecting him to be back in the thinking.
“Boydy had a niggle, a bit of tendonitis, so it was common sense to make sure he was fine.
“The rest has sorted it and he has trained all week as well.”
Should Arfield and Gudmundsson not make it, Dyche has Boyd and Michael Kightly in the wide areas, but could also use record signing Jeff Hendrick in the role he filled as a late substitute at Sunderland: “He’s played outside of a four or a rough diamond more so in international football.
“I don’t remember him playing there for Derby, but he’s a flexible player and has enough about him to play nywhere across the midfield.”
That may be an option, especially with Joey Barton ready and available after his second debut for the club at Sunderland: “Joey is in contention in general, not just in the cup. He played last week because we felt it was appropriate, and he is in the thinking.”
Burnley go in search of a sixth home win in seven games on Saturday, having claimed 22 of their 23 Premier League points so far this season at Turf Moor.
Dyche said: “We’ve been strong at the Turf for a long time now, backed by a positive fanbase.
“They’ve stuck with the team even if we’ve had a quiet half or moments, and that helps. That positivity goes into the team, and vice versa.”
Jay Rodriguez is likely to make his first playing return to Turf Moor, and Dyche feels he is one of a number of Southampton threats, even without injured former Claret Charlie Austin: “They had a big result against Liverpool on Wednesday, and have good energy, particularly on the counter.
“They are a good side, a lot is made of the centre back van Dijk being worth £50m or so, and he is a very good player, Jay Rod is familiar to the fans...Nathan Redmond.”
Meanwhile, Burnley have been strongly linked in Italy with a €7m move for Inter’s 30-year-old Japan left back Yuto Nagamoto.