Spurs trail their London rivals by seven points in the race for the Premier League trophy, but can cut that gap - at least temporarily - to four points should they defeat the Cherries at White Hart Lane in the Saturday lunchtime kickoff.
Antonio Conte's Chelsea side will then take on Manchester United on Sunday afternoon knowing a slip up at Old Trafford could allow Tottenham back into the title race.
Chelsea have already slipped up this month after they lost 2-1 at home to Crystal Palace although they followed the defeat up with a win at Bournemouth last Saturday - just hours after Tottenham had beaten Watford 4-0 and reduced the gap at the top of the table to four points.
Chelsea goalkeeper Thibaut Courtois urged the leaders to remain calm even if they lose to United on Sunday, but Dier believes Tottenham will have a major advantage over the Blues this weekend because they play first.
In an interview with NBC Sports, he said: "It is always nice to play first.
"That was one of the things that was disappointing about last season, the schedule for us and always having to play catch up. That’s quite difficult.
"Hopefully we can narrow the gap to four points and then hope for them to slip up."
Spurs remained in the title race last season until May, when a 2-2 draw against Chelsea at Stamford Bridge saw the Premier League trophy go to Leicester City instead.
Dier praised his teammates for following up the disappointment of last season by being consistent in the league this term, but admitted that Chelsea have simply been better than the north Londoners.
"Last season we had great spells but I think this season what you’ve seen is consistency," he said.
"If we’re talking about our Premier League season as a whole, we’ve been consistent and I can’t really see a patch where we’ve been through a bad spell.
"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.
"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."