They tried to "extend" their influence over the Indian oceans and South-East Asia and had relations with the Aceh Sultanate in Indonesia.
There is a book called The Ottoman Age of Exploration that could interest, I think India and Indonesia acted as "America" for Ottoman Empire, a new land to look at and extend influence.
If I remember correctly it was because of the Ottomans controlling the silk road in the middle east that western countries started sailing west. Specifically Spain for pushing the Moors out of Spain, the Ottomans didn't like that and wouldn't let them trade with Arabia and China. What else did Spain have to do but sail west to China.