TheMirror says United are considering a final huge take it or leave it £60million offer for Dier.
But United fear their hopes of landing the England international are fading as Spurs continue to hold firm.
Boss Jose Mourinho has been harrying executive vice-chairman Ed Woodward for signings all summer after coming sixth in the Premier League last term.
Mourinho thought he could prise Dier away from North London with a bid of around £40m and an offer to double his wages.
But Spurs have stubbornly refused to sell and recently stressed they are prepared to resist all bids for Dier.