Former mayor of New York City, and Everytown founder, Michael Bloomberg speaks on stage during a forum on gun safety at the Iowa Events Center on August 10, 2019 in Des Moines, Iowa. The event was hosted by Everytown for Gun Safety.

Facebook is concerned about a lack of transparency in how Mike Bloomberg's field organizers are using the platform to advocate for his presidential campaign, without identifying that they work for him, according to a source at the company. The source said Facebook is considering taking steps to make it clearer that the people posting messages of support are paid employees.

Facebook has taken a range of steps to improve transparency around political advertising since the Cambridge Analytica scandal in March 2018. A New York Times report revealed that the political consulting firm improperly obtained information about Facebook users, then used that information to target political ads supporting Donald Trump's 2016 presidential campaign.

Among other changes, Facebook now tags all political and issue ads, keeps a library of them and has built an interactive database of all political and issue ad purchases.

Enter Mike Bloomberg, who has spent $48.5 million on campaign and issue ads on Facebook since last May, according to Facebook's Ad Library. Bloomberg's campaign is hiring more than 500 deputy field organizers, a job which includes mobilizing supporters for get-out-the-vote efforts and engaging friends to support Bloomberg for president — which can include sharing on social networks.

But Facebook is concerned about the lack of transparency around Bloomberg's employees' unidentified posts and doesn't want to undercut all the work the company has done around transparency by allowing a campaign to circumvent Facebook's rules, this source said.

This follows last week's news from Facebook when a company spokesperson told CNBC that Facebook would not put political posts from influencers into its ad database, even if a candidate paid the influencer for the post. However, the spokesperson said the posts would go in the archive if the influencer paid to promote it.

Facebook says it communicates with all the campaigns, urging them to follow best practices, including having people posting on behalf of campaigns make it clear in their posts and profiles who they're working for. But Facebook currently has no means to enforce that kind of disclosure. Now, Facebook is exploring different ways to add more transparency about posts to make it clear if a person posting has a paid relationship with a campaign, the source said.

"We think it's important that political campaigns have the guidance and tools to be transparent," a Facebook spokesperson told CNBC. "That's why we recommend campaign employees make the relationship clear on their accounts. We welcome clearer guidance from regulators in this area."

Facebook is referring to the Federal Election Commission. The FCC's regulations around internet communication were last updated in 2006.

Bloomberg's team confirmed his investment in staffers to spread the word on social media.

"We are meeting voters everywhere on any platform that they consume their news. One of the most effective ways of reaching voters is by activating their friends and network to encourage them to support Mike for president," Sabrina Singh, the Bloomberg campaign's senior national spokesperson, said in a statement.