Guinness Premiership strugglers Saints head to Galashiels knowing that a bonus-point victory could be enough for one of two best runners-up spots.
Biarritz, with a maximum 25 points from five games, will wrap up Pool Six one week inside the distance if Northampton lose tomorrow or win without collecting a bonus point.
But Northampton, despite poor Premiership form that has seen them collect just four victories from 12 starts, still look a strong bet to progress.
Borders are already out of the quarter-final picture, and Saints will arrive at Netherdale refreshed by an unexpected break after last Sunday's scheduled league encounter against leaders Bristol was postponed.
Grayson said: "Last weekend's game could not have been played, so it has given us an opportunity to rest a few players, but then playing in the mud may have been an equaliser and given us a chance.
"But the break has given some aching bodies some time to have some positive recovery and to turn our minds quickly to Borders.
"The forecast for Sunday is high winds on a boggy pitch, so it makes the scrum a bit more of a lottery and slows the game down, but we know we have to do a lot of things right to get what we want."
Grayson welcomes back scrum-half Mark Robinson following his recovery from knee trouble, while Johnny Howard lines up on the wing as Ben Cohen and Robbie Kydd forge Saints' midfield partnership.