Ross, 27, scored 13 goals in 23 appearances in all competitions for Manchester City, while Weir, 21, was Liverpool's leading league scorer with seven goals in 16 games.
Weir is also among the nominees for young player of the year.
Ross, capped 103 times, won the Women's Super League and FA WSL Cup with City last season.
Scotland duo Jane Ross and Caroline Weir are in the running for the Women's PFA players' player of the year award.