Unlike Facebook which bases its income on ad revenue, Telegram is funded by user donations, and includes features like encrypted end-to-end messaging.
Facebook-owned Instagram and Whatsapp experienced similar issues.
Bloomberg News reported that Facebook was considering refunds for advertisers whose messages could not be delivered.
After staying tight-lipped on the cause of the outage for almost 24 hours, Facebook early Thursday afternoon blamed it on a "server configuration change that triggered a cascading series of issues".
Millions of users were affected, and thousands took to Twitter on Wednesday and Thursday to complain under the hashtag #facebookdown.
Shares declined 1.8 percent in NY, and have jumped 32 percent this year through Wednesday's close. As of Thursday morning, the only good news for Facebook is that plunging stock price appeared to have found a floor.
Facebook suggested there was nothing new in the New York Times report.
"Yesterday, a server configuration issue made it hard for people to access our apps and services".
A spokesman for the social network said the company was cooperating with investigators in multiple federal probes, without addressing the grand jury inquiry specifically.
The newspaper said the companies had access to user data that Facebook previously said was inaccessible. "We are very sorry for the inconvenience and we appreciate everyone's patience". The interruption also affected gameplay for owners of Oculus VR headsets, a company that Facebook bought in 2014.