Three sources familiar with the Qatari discussions told NBC News the officials feared that handing over the information would harm relations with the Trump administration.
Several US media reports have explored connections between Lebanese-American businessman George Nader and Republican donor Elliott Broidy, who allegedly participated in the secret meetings, and their connections to the UAE and Trump associates.
Qatari officials considered talking with Mueller earlier this year about Nader and Broidy working with the UAE to turn Trump against Qatar, but decided against it, media reports added.
Mueller is investigating allegations that Russia interfered in the 2016 US presidential election, as well as accusations of collusion between Moscow and the Trump campaign.
Russian officials have repeatedly denied all allegations of interference, calling the accusations "absurd." Trump has also denied any collusion between himself and the Kremlin.