"Next year we can have a real go at a Big Game II and maybe fill Twickenham - I really think we can," said Evans, whose side came back from 23-9 down to share the spoils against the Tigers thanks to a last-minute try from Ugo Monye and a touchline conversion from Nick Evans.
"We were capped at 50,000, which meant we sold out a week in advance."
That cap could be removed for the December 2009 fixture, meaning the Londoners could create another record attendance.
Quins have agreed a three-year deal to stage a fixture at Twickenham and the success of the first instalment means there is plenty of optimism surrounding the two remaining fixtures.
"I wonder how many we would have got?" added Evans.
"We didn't have a walk-up and we didn't have last-week sales, which are usually in five figures.
"We have a three-year deal with the Rugby Football Union. Big Game II will happen, Big Game III will happen, and we hope by then we will establish it as the big London Christmas sporting event."