"Of course we couldn't win them all but in general our play has been very positive, and I am sure there are plenty who won't want to face us," Dier told reporters in France, where England also drew against Russia before beating Wales.
"We shouldn't be fearful of anyone... that's the wrong word. We'll wait and see, but we should not fear anyone."
England goalkeeper Joe Hart echoed Dier's sentiments and praised the performances of his side in the tournament.
"We're going to look to build on three good performances. Result-wise it's not been great but performance-wise, I don't think anyone will be looking forward to playing us."
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However, Iceland captain Aron Gunnarsson said he would relish the prospect of taking on England if they advanced to the next round.
Iceland, who are second in the group, face Austria in their final pool game on Wednesday, while Hungary take on Portugal.
"Playing against England in a finals would be something special. It would be a dream for every Icelander. We have always looked towards England in the finals," Gunnarsson, who plays in the second tier of English soccer with Cardiff City, said.
"The Premier League is the most watched league in Iceland and the most talked about. It would be memorable."
(Reporting by Ian Rodricks in Bengaluru; Editing by John O'Brien)
