Dennis Wise's side, who reached the FA Cup Final last season, have made a strong start to the season and currently sit in a promising sixth place with seven points from four games.
Whatsmore, the Lions have won their last two, defeating highly-fancied Leicester 2-0 at home, and triumphing 1-0 away at Coventry.
But Reading, boosted by the excellent 2-0 win over Oxford in midweek, are capable of earning all three points tomorrow.
If the Royals were to win tomorrow and complete a run of three successive league wins under Coppell's command for the first time, it would be an achievement to be proud of and would mark the upturn in our fortunes this season.
However, the Reading manager is thinking about winning the game - not winning runs.
"It's not on my mind at all, we're going there just to win the game as we would anyway," said Coppell, speaking to Reading World.
"We're not trying to set a record or make a precedent, we just want a win in isolation. It'll be a stern test physically and mentally. They've brought in two Canadian players and since then they look a different type of threat."
The Royals should have a fully fit squad available tomorrow, despite an intense recent run of matches.
Steve Coppell welcomed Glen Little back into the team on Wednesday night, and the right-winger should start again at Millwall, even though he missed training this morning after his partner gave birth to a baby boy.
Whilst Little is expected to line-up on the right, Coppell must choose either Hughes, Convey or Brooker to play on the left.
Up front, Kitson and Forster should return to the team after being omitted from the starting line-up at Oxford.
However, Fozzy is suffering from a minor groin strain, so if he is not fit enough to feature tomorrow, veteran forward Shaun Goater could be handed a first team outing.
Otherwise, the Royals are likely to field the same team that defeated Rotherham 1-0 last weekend.
Meanwhile, the Lions have several fitness concerns going into tomorrow's game. Bob Peeters, Kevin Muscat and Paul Ifill are all set to miss the game through injury.
Andy Roberts is also injured, although is unlikely to feature for the Lions again.
Royals fans should watch out for goalkeeper Graham Stack, on loan from Arsenal and Stefan Moore, brought in on loan from Aston Villa.
Predicted Reading Line-Up: Hahnemann; Murty, Williams, Ingimarsson, Shorey; Little, Sidwell, Harper, Hughes; Forster, Kitson