A party source said low turn out and voter complacency for Labour has left the race "uncertain".
Earlier on Friday reports emerged saying that Shaun Bailey's camp believes it can win the contest.
If the Conservative candidate was to win it would be a huge upset, with polls earlier this week showing Mr Khan with an apparently unassailable lead.
According to Opinium, the Labour incumbent was on course to pick up 48 per cent of first-round votes, compared with Mr Bailey's 29 per cent.
When a candidate in the London contest gets 50 per cent of the votes they are elected mayor.
Labour says voter complacency towards Mr Khan means the race could go down to the wire.
“We always said it would be a close election," the party source told The Independent.
"There is no question we are seeing significant impact from turnout and voter complacency.
"There are still half of London boroughs to count and it’s too early to say anything with any certainty at this stage."
Mr Bailey took an early lead as Tory strongholds began to declare first in London.
But Mr Khan has since made up ground and as of 5pm he had 39 per cent of votes counted against Mr Bailey's 37 per cent.
There remains a long way to go in the election, with around half of boroughs yet to declare.
Ballot counting will continue into Saturday, with a result expected in the evening at the earliest.
If no candidate reaches the 50 per cent threshold in the first round of ballots, then the election will go to a two-person run-off with voters' second preferences taken into account.
The London mayoral race is among a whole series of elections that took place across the UK on Thursday.
Around 48 million people were registered to vote, with local council contests taking place in England and elections to the devolved parliaments in Scotland and Wales.
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