The alleged push is said to have occurred just after 17:00 BST on 15 September.
A post-mortem examination carried out on 29 October was inconclusive and further tests are awaited.
A Met spokesperson said the woman who Mr Arlie is believed to have fallen into was of south Asian appearance. The force added she also fell on the escalator.
Mr Arlie is also understood to have spoken to a woman on a bus travelling from North Greenwich underground station, who gave him a tissue for a cut above his eye.
At the time, he was wearing a black t-shirt, light grey jogging bottoms and had a turquoise and grey Mountain Warehouse rucksack.
He was also carrying a medium-sized black suitcase.
BBC News
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