Right now, no, you cannot. They aren't exposed at the network level and aggregating them there is probably harder than you might expect.
In addition to the factors mentioned in the comment thread about how bugs and feature requests might be considered and prioritized among all the other work we do to keep this site running, one potential factor is, hopefully unsurprisingly, "how many users will this impact?"
Let's take a quick look. Saves aren't exposed to SEDE, so you're going to have to trust and not verify that the data that follows is accurate.
How many users on Stack Overflow have, say, at least 1 saved post? The tail is long so I stopped at >= 5:
| 1 save |
2 saves |
3 saves |
4 saves |
5+ saves |
| 25,811 |
3,205 |
958 |
474 |
1,117 |
We're already at a very small number even at a single save, and this includes bookmarks that were converted to saves (so the user may not even be aware). 32K out of 4.04 million users who have been active since August 1st - that's about 0.78% of the active user base that are even using the feature at all, on the busiest site on our network.
Why do I care about how many saves they have in Stack Overflow? Because it's a guidepost for how many they may need to manage across the entire network (and hence how useful a global list might be, if there were some easy and efficient way to present one). I was expecting the first column to be higher, and only segregated because a larger number would be really hard to cross-reference across 350+ other network sites, and would take two weeks to collect. Which should give a hint about why this would be hard to implement if the feature were popular.
Now, let's see how many of those users have at least one save on at least one other site in the network:
Well, 0.21% is not a lot. This is by no means a suggestion that the team has considered this evidence, or would decide based on this evidence, or whether or not this is even on anyone's radar (never mind backlog). But it's damning if you consider that most software companies should prioritize time and effort on features that are used by, well, more than half a percent of its user base.
Again, this isn't an official response. I ran off and captured these metrics independently and have only shared them here, merely to suggest that feature usage should probably be taken into account when deciding where to spend valuable and scarce engineering resources. Also I spent about two hours collecting these metrics and crafting this answer, to which many people on meta would say, "Aaron could have skipped answering the question and just implemented the feature!" Unfortunately software is like a lot of industries, where you can't just swap warm bodies out and expect them to be capable of the same tasks, with similar quality, in a similar timeframe, and without disastrous results - when a pilot is needed for a flight, and they're sick, you can't just take an air traffic controller or gate agent, shove them in the cockpit, and wish them luck.
More breakdown for the stat-hungry (I found the last column interesting because it shows that the people who like saves really like saves a lot.)
which means this simply won't be done- I think that's a bit harsh. We talk about implementing a lot of things, but unfortunately there are only so many engineers and so many meta requests it's really an impossible task to reach any kind of success rate that will make meta folk happy.