The conversation took place at the Republican Governors Association meeting in Florida, Hogan said. It included Pence, the governor of Indiana, and Gov. Chris Christie of New Jersey on the week after the election.
"Mike Pence and Chris Christie are probably the two guys I'm closest to among the Republican governors," Hogan said Wednesday.
Hogan backed Christie's presidential bid and declined to endorse the Trump-Pence ticket in the election.
Hogan did not reveal details about the conversation but mentioned they discussed infrastructure needs for the state.
The governor publicly disavowed Donald Trump during the election, but congratulated Trump after he was elected president.
Trump will attend the Army-Navy game in Baltimore Saturday. Hogan confirmed he also will attend the game, but implied he did not plan to meet with Trump.
"If the opportunity presents itself, I'll certainly welcome him to the state, as I would with any president," Hogan said.