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And organisers have had to shelve plans to close certain parts of the stadium, with tickets being taken up at record levels.
Leinster report selling upwards of 1000 tickets a day through their website, numbers that mean this will be Leinster's biggest ever crowd.
"We are delighted with the response from both on our website, www.LeinsterRugby.ie, and through the twenty retail outlets in Dublin and throughout the province. Interestingly, we have noticed the demand for stand tickets is five times greater than for terrace tickets.
"We opened the West Upper Stand for ticket sales yesterday and over 4,000 out of the 6,100 tickets there are now sold too. Next week we will review the situation and we may then open the North Terrace," said Leinster chief executive Mick Dawson.
"This set to be our biggest ever attendance. We were involved in the Celtic League final v Munster in 2001, there were 30,000 at Lansdowne Road, but this is set to surpass even that," said Leinster media manager Tom McCormack.
The match seems destined to see the biggest ever Heineken Cup quarter-final attendance, surpassing the 35,800 crowd that watched Toulouse beat Montferrand 31-18 in 1999.
