It's possible with the Stack Exchange Data Explorer for bounties which were posted between 8 and 7 full days ago, so could be in their grace period. Since SEDE is updated only once a week, on Sunday morning, we'll miss questions where the bounty has already been awarded later this week. Still, this query produces only 64 questions on Stack Overflow, and most of them are still in the grace period, so it's a decent method to get a list of questions with potential bounties in the grace period, at least in the beginning of the week.
The main challenge with SEDE queries for purposes like this is that SEDE will cache the results until the end of the week. However, it is possible to break the cache.