WASHINGTON—Special counsel Robert Mueller has asked questions about the work of a private consulting firm that has undertaken projects for the United Arab Emirates, according to people familiar with the investigation, suggesting his probe is looking more deeply at foreign influence in Washington.

The questions by Mr. Mueller’s team concern a private consulting firm, Wikistrat, as well as two of its co-founders, Joel Zamel and Daniel Green.

Wikistrat—which was founded in Israel in 2010 and today is based in Washington, D. C.—bills itself as a crowdsourced consulting firm that draws on a large network of experts to help analyze geopolitical problems on behalf of corporate clients and governments.

Marc Mukasey, a lawyer for Messrs. Zamel and Green and Wikistrat, said that his clients aren’t a focus of the probe.

“Joel is a bright young businessman and Wikistrat has been privileged to serve several U.S. government clients,” Mr. Mukasey, chairman of white collar defense at the law firm Greenberg Traurig, said in a statement. “Joel and Wikistrat have only a tenuous connection to the special counsel’s investigation and are cooperating fully.”