Khedira, 32, was at the Emirates Stadium on Sunday for the pre-season friendly defeat to Lyon.
Unai Emery played down speculation the German was set to join Arsenal.
But, according to Italian football journalist Tancredi Palmeri, Khedira is on the brink of a move.
“Khedira close to join Arsenal,” Palmeri wrote on Twitter.
Khedira is under contract at Juventus until the summer of 2021 but struggled for regular minutes last season due to injury.
He has been pushed further down the pecking order following the Serie A champions’ swoops for ex-Arsenal ace Aaron Ramsey and former PSG star Adrien Rabiot.
As a result, Juventus could be willing to offload Khedira for a nominal fee to ease their rising wage bill.
Despite Khedira’s presence at the Emirates Stadium, Emery attempted to shut down the idea of a transfer.
“Khedira is a very good player but this is the first time I have heard his name mentioned,” he said.
Stay up to date with all the big headlines, pictures, analysis, opinion and video on the stories that matter to you.
Follow us on Twitter @DailyStar_Sport – the official Daily Star & dailystar.co.uk Twitter account – providing real news in real time.
We’re also on Facebook @DailyStarSport – offering your must-see news, features, videos and pictures throughout the day to like, comment and share from the Daily Star, Daily Star on Sunday and dailystar.co.uk