Sandeep, who was picked for the World League Round 3 (Semi-Final) played at Rotterdam, Netherlands last month, was dropped yet again after India's dismal show in the event.
Shivendra also failed to fins favour in the list of probables, who will train in Bangalore from July 16 to August 16.
The Asia Cup, which is into its ninth edition, will be held in Ipoh from August 24 to September 1.
Hockey India Selectors B P Govinda, Savitri Purty, Chief Coach Michael Nobbs and Scientific Advisor Jason Konrath alongwith Government Observer Harbinder Singh selected the core probables.
The Asia Cup is also the qualification tournament for the FIH Men's World Cup to be played in The Hague, The Netherlands from May 31 to June 15 next year.