The £28m-rated forward will be Tottenham's top target if new boss Tim Sherwood can recoup funds from flop duo Nacer Chadli and Etienne Capoue.
The pair arrived over the summer, the former for £7m from FC Twente and the latter from Toulouse for £9.3m.
But Sherwood has not been convinced by their performances and is willing to cut them loose at the end of the campaign.
The report claims Everton would be willing to take Chadli while Rafa Benitez at Napoli is keen on French international Capoue.
Should Sherwood successfully trim the wage bill - Jermain Defoe is already off to the MLS and Lewis Holtby has been tipped to leave White Hart Lane as well - then the Tottenham boss will train his attentions on Reus.
The Germany international has been heavily linked with both Arsenal and United, but much will depend on Dortmund's willingness to sell.
They're set to lose Robert Lewandowski and Mario Gotze in back-to-back summers, so they will be desperate to keep Reus, already a star at 24-years-old.
The report notes Spurs would not move for Reus until the end of the season, although that may be too late with United, Tottenham, Arsenal and a host of other top clubs engaged in a fierce battle for a vital top four spot and a place in next year's Champions League.