It is very challenging to design the capacity-approaching labeling schemes for large constellations, such as 32-QAM, in delayed bit-interleaved coded modulation (DBICM). In this paper, we investigate the labeling design for 32-QAM DBICM with various numbers of bits delayed by one time slot. In particular, we aim to obtain the labeling schemes with a high DBICM channel capacity by searching the possible labeling schemes. To reduce the search space of the candidate labeling schemes, we propose the criteria that are necessary for good labeling. Based on the proposed criteria, a three-step search algorithm is proposed to obtain the candidate labeling efficiently. Numerical results demonstrate that the DBICM with our proposed labeling scheme can approach the capacity of 32-QAM within 0.015 dB at an information rate greater than 2.5 bits/symbol.