The 18-year-old, who has been linked with English trio Liverpool, Manchester City and Manchester United, has become a first-team regular for the Bundesliga outfit since joining from boyhood club Birmingham City in 2020.
According to The Sun, all three clubs are keen to recruit Bellingham next year, however any potential Premier League buyer is unlikely to sign him in 2022.
As Dortmund striker Erling Braut Haaland is also a target for several elite teams in Europe, the German club are not prepared to sell both players in the same transfer window.
Haaland's £68m release clause will become active next summer and so his departure is more likely than that of Bellingham, who is valued in excess of £100m.
Bellingham, who still has four years remaining on his contract, has made a bright start to the new campaign, scoring two goals and providing four assists in seven appearances across all competitions.