A short update on the official PlayStation Blog has indicated that it will be "at least a few more days" until the PlayStation Network is back online.
Identical messages on both the European and U.S. blogs state:
"I know you all want to know exactly when the services will be restored. At this time, I can't give you an exact date, as it will likely be at least a few more days. We're terribly sorry for the inconvenience and appreciate your patience as we work through this process."
Previously Sony has indicated that the service will be fully operational by May 31, but unofficially a number of sources are reporting that Sony hopes to have online play up and running much earlier.
The closest to an official confirmation of this comes from Sony Computer Entertainment Europe community manager "MusterBuster", who wrote the following on Twitter:
"Once again, 31st May is the date for FULL restoration of PSN services. Restoration is phased. Online gaming will return BEFORE May 31st."