I wish RE4make's ending had had different cinematography, because Leon's expression is doing a LOT of story/characterization work that we don't get to see without free cam.
His eyes drop with guilt, and he almost frowns when Ashley first says, "I can put a word in with my dad." But when she finishes her thought and actually extends the offer to get him assigned to her detail, his face completely changes. He turns away from her so that she can't see the way his expression becomes a mix of wistfulness and flattery.
At this point in the timeline, Leon is still being held under duress by the government for the sake of Sherry's protection. He can't act out of turn or advocate for himself in any way. So, when Ashley first mentions her dad, Leon knows instantly that he's going to have to lie to her in some way to convince her not to say anything -- because the absolute last thing he needs is for Ashley to start talking about him to her dad.
But then he hears Ashley's actual offer to aid him in a transfer (instead of just generally "putting a good word in" for him), and it's probably the first time since Raccoon City that anyone ever offered to change his circumstances or help him in any way. So, he takes a few precious seconds to actually indulge himself in that fantasy -- to imagine what his life would be like if he actually said "yes."
He knows he can't actually agree to something like this, but it's plain to see that he wants to. So, he sidesteps having to give her a direct "no, I can't" (because that would be suspicious) by offering some words of encouragement and following them up with a stupid joke.
If we'd actually gotten to see his face more clearly in this scene, it would've really hammered home how completely trapped Leon is by his current situation -- and how badly he wishes his life could be different.