The former City pair are amongst the 15 nominees for the honour, with two names to be announced on 22 April.
The two inductees will be decided through a combination of the public vote, in conjunction with votes from the Premier League Awards Panel and those of past inductees into the Hall of Fame.
Voting is now open and will close at 12:00 BST on Monday 8 April.
This is the fourth season of the Hall of Fame, with ex-Chelsea and Arsenal full-back Ashley Cole the first inductee inductee of 2024.
He joined 21 former players and managers including City men Sergio Aguero and Vincent Kompany.
Silva made 309 Premier League appearances over 10 seasons, scoring 60 goals and laying on 93 assists as he lifted the title four times.
The Spaniard was also named in the PFA Team of the Year in three campaigns and is now celebrated with a statue outside the Etihad Stadium.
Toure played 230 games in the Premier League, scoring 59 goals and creating 32 for his team-mates. He won the league on three occasions before leaving in 2018.
An imposing but elegant midfielder, Toure was honoured in the PFA Team of the Year twice.
Other former City players on the shortlist include Andrew Cole and Robbie Fowler.
