Qualifying for the Champions Cup is the minimum requirement for Bristol this season, says director of rugby Pat Lam.
The Bears are currently ninth in the Premiership table, with only the top eight teams progressing to Europe's elite tournament.
They are competing in the Challenge Cup this season - Europe's second-tier competition - after finishing 10th in the league last year.
They are three points adrift of eighth place with 10 games to go.
"The minimum is Champions Cup, we've got to be playing Champions Cup rugby next year," Lam told BBC Radio Bristol.
Bristol reached the round of 16 in the Champions Cup in 2020-21, their first time in the competition in 13 years, and matched that feat last season.
Yet a disappointing league finish dropped them back into the Challenge Cup, a competition they won in 2020.
They are unbeaten in the competition as it stands and play Clermont Auvergne on 31 March in the round of 16.
They next face Northampton at home in the Premiership on Friday, having won their last two league matches against Newcastle and Bath.
"We're in the bottom three - we were bottom before - and then there's the top eight and the top four," Lam said.
"The season has been extremely fractured, big gaps, big breaks. In two months we had four games, now we have four in a row [in four weeks].
"We just looked at it and thought if we win these four that's all we can control - we can't control what other teams do - then 100% we will be in the top eight."
Lam did also not discount a late push for the Premiership top four.
The fight for the play-off places is tight, with only eight points separating Bristol from Gloucester in fourth, with Bristol also having a game in hand on some of the teams above them.
"We knew if we could get through this block of four - we've done two, we've now moved to stage three - that will guarantee we're in that top eight," Lam added.
"We do that and then we can re-evaluate."