A Major League source told Ken Rosenthal of FoxSports.com that Roberts is seeking a four-year contract.
Eligible for free agency after the season, Roberts has been offered three years at $30 million, according to the Baltimore Sun.
The 31-year-old second baseman is a cornerstone for the team.
Retaining Roberts became a topic of discussion this week after the Orioles announced the signing of Nick Markakis to a six-year extension.
"We've made no secret of the fact that we'd love to have Brian come back," Andy MacPhail, the team's president of baseball operations, said Thursday. "We're still working on it. The market hasn't completely played itself out yet. Hopefully we can get something done."
Roberts, one of Baltimore's longest-serving players, has dealt with trade rumors for much of the past two seasons. And those may only intensify if the Orioles aren't able to reach a contract extension with him before the season or by the non-waiver Trade Deadline in late July, a situation that both the player and the team would like to avoid.
Joe Frisaro is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.