The pair caused quite the stir on Wednesday night when they were spotted leaving a dinner date together.
The reality TV star was enjoying a night out with the boy band bachelor when photographers spotted them as they exited Craig's Restaurant in West Hollywood via a back door.
They were pictured leaving the eatery and driving away together; Harry behind the wheel with 18-year-old Kendall by his side in the passenger seat.
Harry, 19, was most recently linked to British supermodel Cara Delevingne, and previously dated US country star Taylor Swift. Kendall, meanwhile, was recently reported to be dating rapper Young Jinsu, following her split from boyfriend Julian Brooks in September.
Their low-key dinner date comes in the middle of a busy week for Harry.
He and his One Direction bandmates are currently in the US promoting their new album Midnight Memories, having landed in Los Angeles on Tuesday night.
This week, they will make a number of high-profile promotional appearances to help get their third album to the number one spot, including a performance at the American Music Awards.
Then, on 23 November — dubbed 1D Day — they will take part in a seven hour live broadcast, featuring special guests including Robbie Williams, Celine Dion and Simon Cowell.
The worldwide extravaganza will take place on YouTube and Google + on Saturday from 7pm until 2am, and will therefore be live as Midnight Memories goes on sale in the UK on Sunday.
"1D Day is all about giving back to our amazing fans for supporting us for the past three years," Liam Payne said. "When we suggested it we never thought anyone would let us loose LIVE all day – we cannot wait!"
As well as guests and behind-the-scenes footage, 1D Day will include exclusive renditions of tracks from Midnight Memories, and even world record attempts.
Perhaps most importantly, the boys will also be dropping in on Google+ Hangouts in an event called the 'One Big Drop In', surprising lucky fans with impromptu chats and the chance to virtually meet them.
One Direction recently completed their huge world wide tour, and will hit the road again in May 2014 when they start their UK stadium tour.