The former Ukip leader, who lives in Bromley, south-east London, last night said he was thinking about running in the 2020 mayoral election.
Outspoken Brexiteer Mr Farage said such a move would be an opportunity to “make arguments” on a high-profile platform.
He believes he has enough support in the capital to beat whichever candidate the Conservatives put forward.
This would throw up the prospect of a head-to-head battle between Mr Farage and Labour’s Mr Khan, a staunch Remainer.
Nigel Farage is currently a member of the European Parliament but will lose his seat when Britain leaves the EU next March.
He told the Financial Times: “I have been encouraged to stand by a group of people, but that doesn’t mean I’m going to.
“I haven’t said no to it, I’m thinking about it.
“The Tory party are very actively aware that if I did stand, they would probably come third, and they are afraid of that.”
Around 1.3 million Londoners voted to leave the EU in the 2016 referendum, while 2.3 million backed Remain.
Next month the Conservatives will pick their candidate to stand against Mr Khan in the 2020 election.
The Tory hopefuls are relatively unknown: London Assembly members Shaun Bailey and Andrew Boff, as well as Ealing councillor Joy Morrissey.
A senior Tory official said Downing Street was braced for electoral “embarrassment” if Mr Farage enters the race.
A ally of the ex-Ukip leader said: “The three Tory candidates are so poor, no one expects any of them to win.
“If you have televised hustings it would just come down to Nigel versus Sadiq.”
Mr Farage has previously criticised Mr Khan over London’s soaring crime rate.
Speaking in March, the MEP hit out at the mayor over alarming statistics showing London’s murder rate had surpassed New York’s.
He suggested Mr Khan should focus on tackling crime instead of wading into debates over US leader Donald Trump.
He said: “I’d never thought I’d see the day where the murder rate in London would overtake that of New York.
“I wonder whether Sadiq Khan should spend a bit less time slagging off Donald Trump and a bit more time getting to grips with crime in London.
“Clearly we have a really bad problem.”
Recently in Khan’s London, a deranged woman terrified children by running after them carrying a knife and shouting ‘I want to kill all you Jews’.
She was arrested after the incident in Stamford Hill in Hackney, London, where there is a large Orthodox Jewish community, reports the Times of Israel.
The woman, 47, was arrested on suspicion of a racially aggravated public order offence and is in custody. Jewish neighbourhood watch group Shomrim said it happened last night, and they alerted police.
Photos they shared online showed a knife lying on the pavement where it was dropped, along with police and Shomrim volunteers responding.
In a statement, the Met Police said:
‘Police were called to Craven Park Road, N15 at 9.04pm on Sunday, 17 June to reports of a woman in possession of a knife behaving erratically.
‘Police attended and the woman, aged 47, was arrested on suspicion of a racially aggravated public order offence. ‘At this time, the female remains in custody at an east London police station. She is expected to undergo a mental health assessment in due course. ‘This incident is not terror related.’
Of course it’s not terror related in the barbarian occupied nation of Britain. At least that’s what their politically correct government is trained to say. How sad to see the once mighty British Empire fall to such depths.
— Shomrim (Stamford Hill) (@Shomrim) June 17, 2018
James E Windsor, Overpasses News Desk
August 30th, 2018