The Red Devils are due at Wembley Stadium on Wednesday for a heavyweight Premier League encounter between two top-four hopefuls.
Sanchez could be handed his top-flight debut for United in that fixture, having made his bow in an FA Cup fourth-round clash with Yeovil.
If he does figure, then the ex-Arsenal man will pose a considerable threat to former north London foes Spurs, but Dier is eager to point out that Jose Mourinho’s side are about much more than “one player”.
The England international told reporters ahead of an eagerly-anticipated fixture: "The game as a whole won't change because of one player.
"[Sanchez playing] doesn't make a difference to me as a player. I've played against him many times and we all know the quality he has.
"But he's going to add to a Man United squad that is already full of quality. It's going to be a great game, a difficult game, but I don't think one player changes a football match.
"Every game is really important now. It really doesn't matter. The Newport game is just as important as [United and Sunday's trip to Liverpool]."
While Sanchez helped United to sweep past Yeovil 4-0 in cup competition, Dier and Spurs were held to a surprise 1-1 draw by League Two outfit Newport County.
A replay in that encounter has now been added to an already hectic and testing fixture list.
After facing United, Mauricio Pochettino’s side head to Anfield to take on Liverpool.