The new update - which was announced on Thursday (07.03.19) in a Twitter Safety channel post including a GIF step by step demonstration of the process.
It's said the development will allow users to specify what type of content is violating their privacy, and whether the tweet reveals their home or physical address, contact information, financial details, ID numbers or a government-issued ID.
In a tweet the company revealed: "We want to move faster in reviewing reported Tweets that share personal information. Starting today, you'll be able to tell us more about the Tweet you are reporting."
The update comes after Twitter revealed in January that private messages sent by users of the micro-blogging platform's Android app could have been exposed publicly.
The company has acknowledged that it has unearthed a security flaw that allowed some tweets that were initially private to become public after the settings were changed to accounts.
In a statement to address the issue, Twitter said: "We're very sorry this happened and we're conducting a full review to help prevent this from happening again."
The popular app also revealed that anyone who updated the email address linked to their account between November 2014 and January 2019 may possibly have had some of their messages exposed.
However, Twitter managed to correct the flaw on January 14 and has pledged to release even more information once it becomes available.