Cooke was the author of an historic British double this year, when she became the first cyclist of either sex to win both the Olympic road race title and the World road race championship in the same year.
Cooke, winner of the BBC Wales TV award in 2003, is joint favourite with boxer Joe Calzaghe, the two-weight world champion who won the BBC Wales award in 2006 and 2007.
Thomas won his Olympic gold in the Team Pursuit. The other three nominees are: Tom James, Olympic gold in the rowing; David Roberts, four Paralympics gold medals in swimming; and Shane Williams, who led Wales to a second rugby grand slam victory.
To vote for your choice of candidate dial 09015 222 80 and then dial 2 for Cooke; or 5 for Thomas. Telephone lines are open now until midnight, Saturday, December 6.
The BBC Wales awards ceremony will take place at the Swalec stadium in Cardiff. The national BBC TV Sports Personality Awards take place the following weekend.