MD of Bangalore-based G G Tronics India Pvt Ltd Narayan Rao Manjunath and alleged middleman Sandeep Goyal have also approached the high court against the trial court order refusing them bail.
The bail pleas will come up for hearing before Justice Hima Kohli.
All the four had been refused bail by a CBI court on July 12.
Singla is alleged to have demanded Rs 10 crore from Kumar, who was recently elevated as Member (Staff) of Railway Board, for shifting him to his choice post of Member (Electrical).
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Kumar, Manjunath and Goyal were not given bail as the court held that they were the main players who hatched the conspiracy.
All the four accused persons have been charge sheeted by CBI for the offence of criminal conspiracy under the IPC and relevant provisions of the Prevention of Corruption Act.
Besides them, six others charge sheeted in the case are M V Murali Krishan and C V Venugopal, Rahul Yadav, Samir Sandhir and Sushil Daga and Ajay Garg.