The 30-year-old. who has won 18 caps for his country, will move to Sandy Park from the Waratahs this summer.
"There's still ambitions to play throughout this year in the June period against the English," Dennis said.
"We'll see how we go there and if that doesn't end up being my last game and I move over to England having played 18 Tests, I'll be grateful for that."
Dennis, who captained the Waratahs until last season, last played for Australia against Wales in November 2013.
"When I negotiated to go over I made the decision that it (international rugby) would be something I'd be giving up," he told BBC Sport from Sydney.
"As hard as it was you probably can't have the best of both worlds in terms of experiencing something different and being in a foreign country, and then also playing for your country."
Dennis is hopeful that he will be able to see out the current Super Rugby season before making the move to Devon in time for the start of the 2016-17 Premiership campaign.
"Ideally I can see out the season with Waratahs and get over in time for pre-season with the Chiefs. It'll mean my season will go for about 18 months this year, but that's fine," he added.
"It'll be a lot of rugby and as long as I can get over there with enough time to acquaint myself with the team and learn the way they play the game in time for the trials, and then kick-off the Premiership later in the year, then that'll be enough."
Exeter's new flanker Dave Dennis wants to play for Australia against England before joining the Chiefs next season.