Currently fourth in the RaboDirect PRO12, Anscombe's troops take a lot of heart from their recent win over European powerhouses Munster in the league.
And Kiwi Anscombe is confident that there is more to come when they take on the might of Leicester.
"You've got to have a great deal of respect for histo ry," the coach said regarding the Tigers' European record.
"But that's not these teams. The challenge is not to beat history, it's how we perform on the day.
"You can't play a semi-final or final here, so you've got to win somewhere away from home so what better way to start than at Welford Road ?
"They're not dissimilar to Munster and we did a job on them so we've got to believe we can do it again."
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