Midfielder Alli has found himself on the periphery of the first team under Jose Mourinho and was linked with a loan move to Paris Saint-Germain during the previous transfer window.
That move did not materialise in the end, though Alli's future was further cast into doubt when he was one of four players hooked at half-time during last week's 1-0 loss to Antwerp in the Europa League, having been picked to make his first appearance in almost a month.
Alli has played just six times for Spurs this season, scoring once in the Europa League, but fellow England international Dier has backed his club colleague to still play a big role for Tottenham this term.
"Yeah, of course Dele has the capacity, we all know his quality, we all know what he brings – he's shown that in the past," Dier said.
"It's really up to him to put in the work, the effort, the commitment and I'm sure he will do that.
"That's who he is, he's always had that drive. It's up to him, it's in his hands and it's in all of our hands.
"Individually, we all have to perform, we've got a very big squad and we all have to perform at the highest level if we want to play."
Spurs rebounded from their disappointment in Belgium by defeating Brighton and Hove Albion 2-1 on Sunday, a result that leaves them just two points adrift of leaders Liverpool in the table.
The situation could quite easily have been even better for Mourinho's men, as they conceded a last-gasp penalty to draw with Newcastle United and surrendered a three-goal lead in a 3-3 thriller against West Ham.
But Dier says there is a belief among the squad that they can win any game they go in to, home or away.
"We're happy with where we are but we could be happier. If you look at some games - the Newcastle game with the penalty was very difficult to understand," Dier said.
"The Everton game wasn't acceptable and then the West Ham game was the same, [it was] really frustrating to be 3-0 up and it was really important for us to get off the mark at home, get the win.
"Obviously we've improved massively away from home which was really our downfall last season.
"It's great to be up and running with a win at home now and we'll just look to keep working hard, keep pushing forward.
"It's very early on but our motivation is clear. For us, we're going into every game to try and win. We know that's not possible but that's our ambition. We're going into every game, no matter the competition believing we can win."