Having already successfully navigated three qualifying rounds, Steven Gerrard's side have just the play-off round remaining before they can challenge in the lucrative group stages of the competition.
Legia will be sure to provide a stern test and head into Thursday's match in Poland undefeated in seven matches.
Rangers though have been no slouches themselves at the start of this season and Daglish reckons they'll have enough to progress.
As quoted by The Sunday Post, he said: "It’s also a huge few weeks for the Ibrox club before the international break in early September. They play St Mirren in Paisley before the Old Firm game a week later.
"In between, they have a tie against Legia Warsaw to negotiate in the Europa League. With a prize pot in excess of £8m up for grabs, it’s vital they get through, and I fancy them to just sneak it."
What are the potential earnings for Rangers?
The money available to the Gers should they make it through could well be vital to the club as Dalglish points out.
As laid out by UEFA.com, just for participating in the groups, the club would receive £2.68m in prize money.
Every win would then net Rangers £522,000, with draws worth £174,000. Finishing top of the group would see another £920,000 received, with the runners up getting £458,000. Just participating in the Round of 32 would then result in another £458,000.
With TV and gate money to be added on top of that, the cash on offer could be instrumental in maintaining the positive direction of Gerrard's Rangers project.
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