I am a Bangladeshi citizen. I shall be travelling to Singapore and Malaysia from December 27, 2013

I am a Bangladeshi citizen. I shall be travelling to Singapore and Malaysia from December 27, 2013 to January 10, 2014. I intend to make a short trip to Mainland China between January 7, 2014 to January 9, 2014. I may not get enough time to submit and get my visa from The Embassy at Dhaka as my passport is with the other Embassies at the moment. May I apply for a tourist L at Singapore?