Dawson injured his left shoulder in the last minute of injury time in the Wanderers' defeat of the Leicester Tigers Extras in a Zurich A League match on Monday, January 19.
The match was supposed to mark his return to fitness following a calf strain he suffered against Leicester Tigers on December 20.
Northampton Saints team manager Lennie Newman said: 'We hope Daws will start the game on the bench subject to a fitness test at our captain's run on Saturday.'
The starting XV remains unchanged from the team that beat Agen at the Stade Armandie last Friday.
Saints need to win Sunday's game to qualify for the quarter-finals whereas Llanelli could get through with just a draw.
Head coach Wayne Smith said: 'We all know and respect the Scarlets' record in the Heineken Cup. This is a big game, and we know they are big game players. It is going to be one heck of a contest.'
Sunday's game - KO 3pm - is a sell-out and is being shown live on Sky Sports.
Northampton Saints: B Reihana; M Tucker, C Hyndman, J Leslie (capt), B Cohen; P Grayson, M Robinson; T Smith, S Thompson, R Morris, M Lord, M Connors, A Blowers, D Fox, G Seely
Replacements: D Richmond, C Budgen, J Phillips, M Soden, M Dawson, S Drahm, O Ripol,
Llanelli Scarlets: B Davies; G Evans, M Taylor, M Watkins, S Finau; S Jones, D Peel; I Thomas, R McBryde, J Davies, V Cooper (capt), A Jones, D Jones, S Easterby, S Quinnell
Replacements: P John, A Gravelle, C Wyatt, D Hodges, M Phillips, G Bowen, T Selley,
Referee: Donal Courtney (Ireland)