Hogg won the accolade in 2016 and has enjoyed another excellent tournament, with two tries and a man-of-the-match award in the opening win over Ireland before making key contributions in other games.
Russell scooped two man-of-the-match awards, in the third-round defeat of Wales and again at the weekend when Scotland ended their campaign with a third victory of the year against Italy at BT Murrayfield.
The public vote is now open at www.rbs6nations.com/RBSPlayerOfTheChampionship, closing at midday on Tuesday.
Three members of England’s title-winning team have been named on the shortlist for this season’s RBS 6 Nations player of the championship.
Centre Owen Farrell, lock Joe Launchbury and flanker Maro Itoje have made the 12-strong group.
Players in every Six Nations match were awarded or deducted points based upon several different performance categories which cover all aspects of the game, with former South Africa and Italy coach Nick Mallett also involved in drawing up the shortlist.
Wales also have two representatives in scrum-half Rhys Webb and hooker Ken Owens, with France pair Louis Picamoles and Camille Lopez also being nominated.
Scrum-half Conor Murray and flanker CJ Stander fly the flag for Ireland, with the list being completed by Italy captain Sergio Parisse.
The award has been dominated by Irish players since it was launched in 2004, with Brian O’Driscoll taking top honours three times.
NOMINEES FOR PLAYER OF THE CHAMPIONSHIP
1 Louis Picamoles France
2 CJ Stander Ireland
3 Finn Russell Scotland
4 Camille Lopez France
5 Maro Itoje England
6 Owen Farrell England
7 Joe Launchbury England
8 Stuart Hogg Scotland
9 Conor Murray Ireland
10 Sergio Parisse Italy
11 Rhys Webb Wales
12 Ken Owens Wales