Khan, whose parents were born in India and lived in Pakistan before emigrating to the United Kingdom, responded immediately by saying: "Home's south London, mate".
Mayor of London Sadiq Khan arrived in Lahore via the Wagah border on an official visit on Wednesday, with the message that many Indians wanted good relations with Pakistan.
Last June, in answer to a question from Assembly Member Caroline Pidgeon, Mayor Khan said that while the contract with Overground operator Arriva Rail London contains provision for the service, its introduction would be "subject to staff consultation" and that "the earliest possible date" it could launch would be Boxing Day 2017.
Sharing images from the trip, he tweeted: "Honour to visit the most sacred place in the world for the Sikh faith - the handsome Golden Temple here in Amritsar, India".
During his stay there, Khan had visited Delhi, Mumbai and Amritsar and met with politicians and celebrities.More news: Google's new guidelines will prevent apps from collecting unnecessary user data
The mayor was received by officials from the Punjab government upon his arrival and is now holding a meeting with Chief Minister Shahbaz Sharif in Model Town.
He briefed the Mayor on the excellent opportunities for trade and investment in Pakistan.
The chief minister was quoted as saying that Pakistan had achieved great success in its war on terrorism, and would win it by introducing various socio-economic reforms. "We appreciate the cooperation of British people", he said.
Asked in July of this year for an update, Mr Khan said TfL expected "to be able to confirm the plan for London Overground Boxing Day services in September". "I am happy to know that Pakistan's economy is growing", he said, while thanking the mayor for according him a warm welcome.
Khan was elected the first Muslim Mayor of London and was born in Tooting, south-west London.