Ulster lead the Tigers by two points, who themselves are just a point above Clermont Auvergne in a tightly contested pool.
Leicester came out on top 20-9 when the two sides met back in November but Trimble believes Ulster have made big strides since and is looking forward to Friday night rugby.
"We have come quite a long way since our last match at Welford Road and as our last results have shown we are starting to build nicely and are positive we can take that confidence through to this weekend's match," said Trimble.
"Leicester are a top European side and it was only ever a matter of time until they got their season off the ground, they are a big game side and we know they will be arriving thinking that they can repeat the result at Welford Road."
"This is what it's all about: Friday night, Ravenhill, Heineken Cup - this is why we play.
"I have some fantastic memories of European rugby at home and Toulouse (2006) stands out for me - it was just a brilliant afternoon in Belfast.
"Fortunately we are usually able to put in a performance worthy of the occasion and atmosphere in the Heineken Cup. Our record at home is pretty significant.
"This is a massive moment and I think our season will be defined by our next two games. But we have been slowly gathering momentum and are in a really good position to take Leicester on."