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Self-supervised learning (SSL) methods such as masked language modeling have shown massive performance gains by pretraining transformer models for a variety of natural language processing tasks. The follow-up research adapted similar methods like masked image modeling in vision transformer and demonstrated improvements in the image classification task. Such simple self-supervised methods are not exhaustively studied for object detection transformers (DETR, Deformable DETR) as their transformer encoder modules take input in the convolutional neural network (CNN) extracted feature space rather than the image space as in general vision transformers. However, the CNN feature maps still maintain the spatial relationship and we utilize this property to design self-supervised learning approaches to train the encoder of object detection transformers in pretraining and multi-task learning settings. We explore common self-supervised methods based on image reconstruction, masked image modeling and jigsaw. Preliminary experiments in the iSAID dataset demonstrate faster convergence of DETR in the initial epochs in both pretraining and multi-task learning settings; nonetheless, similar improvement is not observed in the case of multi-task learning with Deformable DETR. The code for our experiments with DETR and Deformable DETR are available at https://github.com/gokulkarthik/detr and https://github.com/gokulkarthik/Deformable-DETR respectively.