The O's and Fowler are believed to be discussing a two- or three-year deal worth about $12 million to $13 million annually.
If Fowler signs with Baltimore, he would likely play right field, where Ryan Flaherty currently sits atop the depth chart.
Fowler, an eight-year veteran, is coming off a productive season with the Cubs. The 29-year-old outfielder played in a career-high 156 games and hit .250. He also stole 20 bases and set a career high in home runs with 17.
Fowler has spent much of his career in the National League, but he hit .276 with the Astros in 2014, his lone season in the American League.
Both Gallardo and Fowler rejected qualifying offers this offseason and will therefore cost the Orioles a Draft pick if they sign. The O's currently possess both the 14th and 29th overall picks.
• 2016 Draft order
Additionally, the Cubs and Rangers, Fowler's and Gallardo's former teams, respectively, would receive Draft-pick compensation for the departing free agents.
William Boor is a reporter for MLB.com. Follow him on Twitter at @wboor. This story was not subject to the approval of Major League Baseball or its clubs.