The youngster, who moved to Germany from Manchester City in 2017, has attracted a number of European suitors with his performances in the senior team.
Since the start of last season, Sancho has netted 15 goals and claimed 19 assists in the Bundesliga, prompting a number of clubs to show interest.
According to the Daily Mail, the 19-year-old has grown unsettled at Dortmund, with the club already preparing for life without the youngster next summer.
It is claimed that Man United and Liverpool, who made no major signings over the summer, have both established firm interest in the player.
United made a concerted effort to sign Sancho over the previous summer, although it was made clear that the youngster was not for sale after just one season in the Dortmund first team.
Next summer, on the other hand, feels like a time when the youngster makes that highly anticipated big move.