Metropolitan Police Commander Jon Savell said closed-circuit television images showed Abdul Ezedi walking on a bridge over the river but never exiting it.
Investigators concluded he had probably "gone into the water", although they haven't found a body.
"At this time of year, the Thames is very fast flowing, very wide and full of lots of snags," Savell told reporters on Friday.
"It is quite likely that if he has gone in the water, he won't appear for maybe up to a month, and it's not beyond possibility that he may never actually surface."
Police launched a nationwide manhunt for Ezedi, 35, after the woman and her daughter were attacked with an alkaline substance in the Clapham area of south London on January 31.
Images of Ezedi captured after the attack revealed he suffered significant injuries to the right side of his face.
The woman had previously been in a relationship with him, according to police.
British media reported that Ezedi was an Afghan refugee who was granted asylum even after he was convicted of a sex offence in Britain in 2018.
Ezedi's asylum application was initially rejected, but he was later given permission to remain in the UK after claiming that he had converted to Christianity, the Daily Telegraph newspaper reported.
Police said their inquiries continue.
