The 25-year-old Davidson played 28 games this season for Edmonton, getting one assist. The Lethbridge, Alberta, native has five goals and 13 points in 91 games.
Desharnais, 30, had four goals and 10 points in 31 games this season with Montreal. Desharnais, from Laurier-Station, Quebec, has played 435 games -- all with the Canadiens -- and has 79 goals and 250 points.
The trade deadline is Wednesday at 3 p.m. ET.
Information from The Associated Press was used in this report.