Mourinho has seen his injury concerns mount in recent weeks, with Zlatan Ibrahimovic and Marcos Rojo joining the likes of Phil Jones, Chris Smalling and Juan Mata on the sidelines following Thursday's extra-time victory over Anderlecht in the Europa League.
Neither Herrera nor Young was involved in that match, but Mourinho admitted that aside from those two he has very few fresh players to pick from this weekend.
"Eric Bailly has played six matches in a row – 540 minutes in a row. We lost Marcos Rojo, we don't have Jones, we don't have Smalling. We are in trouble and, now, we lose Zlatan too but, in attack, we have options: [Wayne] Rooney is coming and let's see if Mata can also return before the end of the season. Let's see what happens," he told the club's official website.
"Herrera plays [against Burnley]. He didn't play on Thursday – one yellow card and he would have missed the semi-finals. I was thinking about him and [fellow substitute Marouane] Fellaini both at the same time but, because I made a change with Marcos Rojo, I couldn't do that and he didn't play.
"So Herrera is fresh to play. Ashley Young is fresh to play and who else? Nobody else is fresh to play! Now we need absolutely everyone and I don't have to think about Axel Tuanzebe going to the Under-20 World Cup in Korea because maybe Axel has to come now. We need everybody.
"[Rooney] has a good mentality, he's a fighter, he's a strong man and, even if he's not in the best condition or not at the level of sharpness that you need to play high-level football, he has the experience and the character."
United travel to Turf Moor knowing that victory would see them temporarily close the gap on the top four to just one point.