Player of the year Barkley was withdrawn before half-time in last weekend’s 3-1 defeat at West Ham that all but sealed the Hatters’ relegation.
A calf injury will rule the midfielder out for several weeks, while an Achilles issue will mean defender Burke will play no part against the Cottagers.
Asked at his pre-match press conference on Friday afternoon on how he will approach the season finale, Edwards said: “We’ll pick a team best suited to win the game.
“We want to end the season on a high, we want to reward the fans for their unbelievable support with a win and three points.
“We want to finish as a high and as many points as we can. We want to find any kind of motivation and try and go into the next season as high as possible.
“We’ll try and win 12-0 and see what happens. But the bottom line is, we want to give a good account of ourselves and reward the fans for the support they’ve given us over the past 37 games.”