The newspaper quoted a person close to negotiations between Merriman's attorney and an NFL official as saying the player would drop the appeal Wednesday.
If the suspension goes into affect this week, Merriman could return to the Chargers for their Dec. 3 game against Buffalo.
Merriman's attorney David Cornwell said Merriman apparently tested positive for nandrolone, an anabolic steroid in a nutritional supplement Merriman uses.
Merriman, who had 10 sacks last season, tied a career high with three sacks in San Diego's 38-24 victory Sunday over St. Louis. He has 8 1/2 sacks on the season, tied with Green Bay's Aaron Kampman for the league lead.
San Diego is 5-2 and tied with Denver for first in the AFC West.