Exeter are capable of reaching the Premiership's end-of-season play-offs, according to captain Dean Mumm.
The Chiefs are currently third in the table, having and in the past three weeks.
Rob Baxter's side have never finished higher than fifth in the top flight.
When asked if a top-four place was within reach, Mumm told BBC South West: "I don't see any reason why not. But the challenge is to maintain it."
He continued: "It's good to get one or two wins against the top four sides, but the real challenge is to do that over a sustained period, and that's what those teams are good at and that's why they've been involved in finals.
"We've put ourselves in a position where the more wins we can get from now on, the more we can break away from the pack in the middle.
"That's going to be a really big aim of ours, to be consistent enough to do that."
To that end, Exeter are seven points clear of fourth-placed Saracens and fifth-placed Leicester, who are now the only side who made last season's play-offs not to have lost to the Devon side this campaign.
Exeter might have beaten Saracens and Northampton when their international players were away, but Mumm says the Chiefs still had to be good enough to beat established top-four clubs.
"You're as good as the team that you play against on the day," he said.
"Maybe we were fortunate to get Northampton and Sarries without their internationals, but we were also good enough to get the result.
"We deal with whatever team they show when their time comes."