Sinha is expected to meet Defence Minister A K Antony to discuss the situation that has emerged after Joshi quit on moral grounds, sources said.
Sinha, who is based in Mumbai, is likely to arrive in Delhi anytime soon.
Seniormost in the Navy after Joshi, Sinha is also in the race for the next chief of the maritime force.
Sinha, Navy Acting Chief, Vice Admiral Robin Dhowan, and Eastern Naval Commander Vice Admiral Anil Chopra are in the reckoning for the top job in the force.
Meanwhile, Antony has cancelled his visit to Goa where he was supposed to inaugurate a shore-based take-off facility for Indian Navy's fighter aircraft such as the MiG 29Ks and the Light Combat Aircraft.
Joshi resigned yesterday after taking moral responsibility and his resignation was promptly accepted by Antony.
The resignation of 59-year-old Joshi, who had about 15 months more left in service, came hours after submarine INS Sindhuratna had a mishap off the Mumbai coast in which seven sailors were taken seriously ill and two officers were killed.