Barrow is one of a growing number of House Democrats distancing themselves from Pelosi as the Nov. 2 election approaches.
He is being challenged by Republican Ray McKinney, a nuclear power plant manager from Vidalia backed by many tea party activists.
Barrow's 12th Congressional District -- which includes a portion of the Augusta region -- has tilted only slightly Democratic in recent years.
Seeking a fourth term, Barrow has long sometimes bucked party leaders, including President Barack Obama.
His spokeswoman, Jane Brodsky, didn't answer directly when asked last week whether he'll back Pelosi if she seeks to keep her post.
"November is a long way off," Brodsky said. "Congressman Barrow doesn't even know who's running."
But Pelosi has offered no hint she plans to step down and remains a key target of the GOP's strategy to wrest back a House majority.
Republican national chairman Michael Steel underscored that point in a recent appearance for McKinney.
"It will take 39 seats to gain a majority in the House and fire Nancy Pelosi," Steele told McKinney supporters at a rally in Statesboro.
Last week, a Rasmussen Reports national poll found Pelosi is the least popular congressional leader - 59 percent of respondents viewed her unfavorably.