Sakho, meanwhile, has been offered an escape route by Mark Hughes and the Stoke manager is hopeful of concluding a deal before the transfer deadline.
Sakho is free to leave Liverpool on a temporary basis after falling out of favour with Klopp.
Klopp ordered the 26-year-old home from Liverpool’s pre-season tour of the United States for disciplinary reasons, while Sakho has missed the start of the season with a heel injury.
It was the latest controversy in a difficult year for the defender, after he was initially banned for failing a drugs test before Uefa exonerated him during the summer.
Liverpool have stressed they have no plans to offload Sakho permanently but want to arrange a loan move for him to build up his fitness.
Hughes is determined to bring in defensive cover, with Stoke conceding four goals against Manchester City on Saturday, and Sakho has emerged as a realistic target.
Stoke have endured a frustrating summer, with only Joe Allen and Ramadan Sobhi arriving so far, but want to make at least two more signings.