The 29-year-old's agent, Gary Greenstin, confirmed to NBC Washington that he's already spoken to the Capitals about a contract extension with the club.
"He's comfortable here," Greenstin said. "Good coaching staff, he fits here very well, but Grabo is very talented center. He's able to play in a lot of organization the same role. He's a first-two liner, he reads the game very well, but we'll see what's happening. Most likely he'll stay here."
In 42 games with the Capitals so far this season, Grabovski has picked up 12 goals and 20 assists for 32 points.
"Coach [Adam Oates] likes him, we just begin talking about future contract," Greenstin said. "It's not easy process. It will take some time, I believe.
"He's very comfortable in Washington... We'll see. Good coach, good organization, we go from this."
Meanwhile, the Capitals continue to shop forward Martin Erat, defenseman Dmitry Orlov and goalie Michal Neuvirth.
Sportsnet analyst and former Tampa Bay Lightning GM Brian Lawton indicated on Twitter that the Phoenix Coyotes are interested in Erat and are in talks with the Capitals about acquiring him.