Dolan also serves as president of the Conference of Catholic Bishops. Peter Flaherty, a Catholic adviser to Mitt Romney and his religious liaison when he was governor or Massachusetts, said the presumptive Republican nominee met with Dolan in April at the cardinal's residence, The New York Times reported, and has been reaching out to him since.
While a majority of U.S. Catholics voted for President Obama in 2008, Flaherty said the Republicans hope to woo many of them to Romney.
"We're going to have outreach to Catholics in a coordinated, organized effort -- state by state, diocese by diocese, parish by parish and pew by pew," Flaherty told the Times.
Dolan has been an outspoken opponent of the Obama administration's policy that religious hospitals, schools and similar institutions must include birth control coverage in their insurance plans.