That ambition is a mark of just how far director of rugby Rob Baxter has brought the club in the space of just two seasons in the top flight of English rugby.
And Exeter can fulfil their aim at a sold-out and raucous Sandy Park on Sunday if they beat Northampton and deny the Saints a bonus point.
"There is a lot resting on this game," said Rennie. "But as happy as the players are to be in the Heineken Cup, which is fantastic, we are all concentrating on this weekend.
"It is a great achievement for the club so far - but we're not resting on our laurels.
"We don't see that as all we're going to achieve this season. This weekend and even next weekend are massive for the club.
"A couple of years ago this club was playing in the Championship and guys may not have thought this was going to happen but there is a good ethos and culture here.
"Everybody is over the moon and hopefully we can keep improving as a side."
Exeter go into the game on the back of four straight Premiership victories, a run which saw them close the gap on the top four and then, last week, overtake Northampton with a last-gasp win against Worcester.
The Saints beat Exeter comfortably at Franklin's Gardens earlier in the season but Sunday's showdown will be a different prospect altogether.
Northampton director of rugby Jim Mallinder is full of admiration for the job Baxter has done at Exeter, with the support of local businessman Tony Rowe.
"Rob Baxter and his coaches have done very well to lead Exeter to be challenging for a play-off spot this season," Mallinder said.
"He has created plenty of team spirit in a squad that is prepared to play all the way to the final whistle, as they showed at Worcester last weekend.
"They have turned Sandy Park into something of a fortress in their two years in Aviva Premiership Rugby and are probably favourites for this game."
Northampton were soundly beaten by Leicester at home last weekend and it is they who are under the most pressure to make the semi-finals, having crashed out of Europe in the group stages.
"There is plenty of determination to put right the wrongs of last Saturday afternoon. All the players have a point to prove and there is a positive mood ahead of our trip to Exeter," Mallinder said.
"We know what the match means to the club and our supporters, and we will be putting in every effort to get the win that we all want."
Northampton have made two changes from the defeat to Leicester, with Stephen Myler replacing Ryan Lamb at fly-half and Mark Sorenson in for Samu Manoa in the second row.
Richard Baxter, son of the boss, will start his 350th league game for Exeter at number eight while Jason Shoemark comes into the centre and Phil Dollman moves to full-back.
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