Sky Sports says Ole Gunnar Solskjaer's side are set to head a long list of clubs competing for the signature of Europe's most in-demand attacking player.
However, the Red Devils know their optimism rests on the need to secure a top four Champions League place this season.
United are able to meet Dortmund's financial demands for the player, while having the power to match any rival's lucrative wage offers.
Dortmund have already made clear their willingness to allow the youngster to leave, though will demand a £120million fee in order to sign off on a deal.
As things stand Solskjaer's men currently sit four points adrift of the top four places, and made up serious ground recently with victory over rivals Chelsea at Stamford Bridge.
The Blues have also been linked with Sancho, who grew up supporting the club as a child in Kennington.