Walsh, whose contract was to come to an end tomorrow, had already submitted his resignation last month after his demands for a greater say in team decisions and hand-picked support staff were turned down by HI and SAI.
He had been negotiating to stay on board and met Sports Minister Sarbananda Sonowal this morning but the talks ended inconclusively, prompting the 60-year-old to head back to Australia without withdrawing his resignation.
However, a fresh proposal will sent to him in the next couple of days for his consideration, leaving the door still open for his return to India.
Walsh, who was present at a press conference, said that he was still optimistic about coaching the Indian team and that the fresh proposal would address all his demands.
Walsh's continuance had become doubtful after reports emerged that he had developed serious differences with Hockey India President Narinder Batra.
Batra had alleged that Walsh had indulged in "financial fraud" during his stint with USA Hockey and he was reluctant to keep the Australian on board.
If Walsh does not come back, it can be counted as a setback to Indian hockey considering that the team had been producing good results under his watch. The men recently won the Asian Games gold medal after a gap of 16 years, which also fetched them qualification for the 2016 Olympic Games in Rio.
Before this, the team won a silver medal in the Commonwealth Games and most recently defeated world champions Australia in an away Test series.
Earlier, a three-member panel had been formed to look into Walsh's demands but it failed to come to any "conclusion".
The panel comprising former hockey captains Ajit Pal Singh, Ashok Kumar and Zafar Iqbal met Walsh, Hockey India Performance Director Roelant Oltmans and Sports Authority of India officials twice but could not come up with a solution to end the logjam.
Apart from a greater say in decisions and support staff of his choice, Walsh has also sought 120 days paid leave in a year during which he has committed to stay available over video conference for players.