Chelsea travel to United with no league wins at Old Trafford since 2013 and Dier is hopeful that the extra pressure of Tottenham's result can cause their London rivals to falter.
"It is always nice to play first... Hopefully we can narrow the gap to four points and then hope for them to slip up," Dier told NBC Sports.
Antonio Conte's side ended 2016 on a league record equalling 13-game winning run stretching back to the start of October, but were beaten 2-0 at Spurs in their first game of the new year.
Dier praised Tottenham's consistency but admitted that Chelsea deserve to be on top.
"It isn't a case of 'we've lost it' but it's a case of Chelsea have done extremely well themselves and went on that amazing unbeaten run," Dier said.
"As a season, we've been consistent and going into the last period now we've been impressive and want to try and keep that up."
(Reporting by Aditi Prakash in Bengaluru; editing by Sudipto Ganguly)
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