Saudi Arabia may try to end anonymity for Twitter users in the country by limiting access to the site to people who register their identification documents, the Arab News daily reported.
Last week, local media reported the government had asked telecom companies to look at ways they could monitor, or block, free internet phone services such as Skype.
Twitter is highly popular with Saudis and has stirred broad debate on subjects ranging from religion to politics in a country where such public discussion had been considered at best unseemly and sometimes illegal.
Early this month, the security spokesman for Saudi Arabia's Interior Ministry described social networking, particularly Twitter, as a tool used by fighters to stir social unrest.
The country's Grand Mufti, Saudi Arabia's top cleric, last week described users of the microblogging site as "clowns" wasting time with frivolous and even harmful discussions, local newspapers reported.
"A source at (the regulator) described the move as a natural result of the successful implementation of (its) decision to add a user's identification numbers while topping up mobile phone credit," Arab News reported on Saturday.
That would not necessarily make a user's identity visible to other users of the site, but it would mean the Saudi government could monitor the tweets of individual Saudis.
The English-language daily and sister paper to the Saudi-owned pan-Arab Asharq al-Awsat newspaper, did not explain how the authorities might be able to restrict ability to post on Twitter.
Both newspapers belong to a publishing group owned by the ruling family and run by a son of Crown Prince Salman.
Internet service providers are legally obliged to block websites showing content deemed pornographic.
'Sending false information'
One of the big investors in Twitter is Saudi Arabian billionaire Prince Alwaleed bin Talal, a nephew of King Abdullah who also holds significant stakes in Citi Group, News Corp and Apple through his Kingdom Holding Company.
The country's telecom regulator, Communications and Information Technology Commission (CITC) did not immediately responded to requests for comment on the report. Last week it did not comment on the report it was seeking to restrict Skype use.
A spokeswoman for Kingdom Holding said Prince Alwaleed was not available to comment.
"There are people who misuse the social networking and try to send false information and false evaluation of the situation in the kingdom and the way the policemen in the kingdom are dealing with these situations," said Major General Mansour Turki, the security spokesman, at a news conference on Mar 8.
At a separate interview with Reuters this month, Turki argued that a small number of supporters of al Qaeda and activists from Saudi Arabia's Shia minority used social media to stir wider sympathy for their goals and social unrest.
However, he also argued against banning the site.
Two weeks ago one of Saudi Arabia's most prominent clerics, Salman al-Awdah, who has 2.4 million followers on the site, used Twitter to attack the government's security policy as too harsh and call for better services.
Two leading Saudi human rights activists were sentenced to long prison terms this month for a variety of offences including "internet crimes" because they had used Twitter and other sites to attack the government.
Some top princes in the monarchy now use Twitter themselves and Crown Prince Salman, King Abdullah's designated heir and also Defence Minister, recently opened an official account.