Norris went 4-3 with a 4.80 ERA in 11 games, including nine starts, for the Orioles last year after he was acquired in a trade with Houston. Over 50 2/3 innings, Norris gave up 61 hits with 24 walks and 57 strikeouts.
In five home games, Norris went 2-1 with a 7.30 ERA and in six road games, he went 2-2 with a 2.42 ERA.
The Orioles acquired Norris in a July 31 trade deadline deal, sending minor league pitcher Josh Hader, outfielder LJ Hoes and a 2014 competitive balance draft pick to the Astros.
Norris earned $3 million last season and MLBTradeRumors.com projected he would make $5 million this season through arbitration.
This leaves the Orioles with five arbitration-eligible players in Chris Davis, Matt Wieters, Tommy Hunter, Troy Patton and Brian Matusz. Clubs and players exchange arbitration figures Friday and if agreements are not reached later, hearings will be held during February.
The O's agreement with Norris was first reported by The Sun.