Whelan, Wilson and Walters are among 36 players named in Martin O'Neill's preliminary line-up for Eire's opening European Championship qualifier in Georgia on Saturday, 7 September, as well as a friendly against Oman four days earlier.
The squad will be reduced in size ahead of the players meeting up in Dublin on August 31 - 24 hours after the Potters face Manchester City at the Etihad Stadium.
Republic boss O'Neill said: "I have had the opportunity to work with the players since last November, and we are well prepared as we embark upon the first of our qualifiers next month.
"Oman will provide a good test to start our trip before we travel to Tbilisi. We are focused on the task in hand, and look forward to the challenges ahead of us."