Indian players are not allowed to play for foreign T20 leagues while they are active in domestic cricket.
Suthar picked 10 wickets in India's test win in Galle, while Jadeja picked 4 wickets in all.
Kuldeep Yadav managed only one wicket in first Test in Galle.
Saransh Jain replaced injured Washington Sundar in India squad for Sri Lanka Tests.
England bowled out Pakistan for 171 runs in first innings and made 112/2 at stumps on day one.
Indian mixed disability team defeated England at the Lord's in a T20 game.