Koulibaly sat out the Blues' 1-1 draw with Manchester United on 22 October with a knee injury, while Cucurella has been dealing with illness in recent weeks.
The latter was substituted in the 36th minute of the clash with the Red Devils at Stamford Bridge.
Potter has revealed that Koulibaly will not be fit in time to face Salzburg (via football.london):
"It's not too serious but this game was too soon for him [Koulibaly]. We're hoping to get him on the grass Wednesday or Thursday."
He then touched on Cucurella's situation, explaining that his substitution in the draw with United was a tactical one:
“He [Cucurella] has had a bit of illness but he is now a lot better. The reason for coming off against Manchester United was purely tactical.”
Both defenders joined Chelsea in the summer from Napoli and Brighton & Hove Albion respectively.
Koulibaly arrived in a £34.2 million deal and was a regular starter under former manager Thomas Tuchel, making six appearances and scoring one goal.
He has played five times under Potter but was benched in the English tactician's first game in charge, which was a 2-1 win over Crystal Palace on 1 October.
Meanwhile, Cucurella was signed for £58.7 million and has made 13 appearances across competitions, providing two assists.
Chelsea have made an impressive recovery in the Champions League this season under Potter
Should Potter's men secure all three points against Salzburg at Red Bull Arena, they would win Group E.
The Blues sit on seven points, one ahead of the second-placed Austrian outfit heading into matchday five of six.
It has been an impressive turnaround in Europe overseen by Potter.
Chelsea were sitting bottom of the group when he took over from Thomas Tuchel on 8 September.
They had just lost 1-0 to Dinamo Zagreb and there were some fans who feared that they would exit the Champions League before the knockout stages.
However, a 1-1 draw with Salzburg and two wins over AC Milan, including an impressive 3-0 victory, have seen the Blues turn things around.
Chelsea are playing attacking football that has been a nightmare for defenders in Europe.
None more so than Milan, who were picked apart at Stamford Bridge on 11 October.
It bodes well for the 2021 Champions League winners, who may be a side to keep a close eye on should they seal Group E.