Manager Steve Clarke says it would be "unbelievable" if Kilmarnock were to achieve European football next season.
With a game in hand, the Rugby Park club are currently seven points behind Hibernian in fourth, which could result in a Europa League spot.
"For us I think it's just to continue what we're doing," said Clarke after picking up a third Premiership manager of the month award in a row.
"Finishing fifth would be great, fourth would be unbelievable."
Killie, unbeaten in 10 league games, meet Hamilton in Saturday's lone top flight fixture before the league splits in two for the run-in.
Fourth place will yield European football unless semi-finalists Motherwell win the Scottish Cup but Clarke thinks it will be a big challenge.
"I think we're too far away from fourth to have such a big chance of finishing fourth," said. "But even if we finish sixth it would still be a big achievement for the club.
"When I came in here in October the only expectation was to stay in the league and we've managed to do that comfortably."
Kilmarnock, who last played in Europe in season 2001-02, were bottom of the table with just three points from eight games when previous boss Lee McCulloch stood down.
While Clarke expects to lose influential January signing Youssuf Mulumbu in the summer, he has been busy building for next season, with several players committing to new contracts already.
"Since I came to the club we've been looking at what we've got, what we don't have, how to improve the squad," he said.
"It's an ongoing process you're always looking at games, watching players. I've got people out all over the country having a look at different people.
"Hopefully over the course of the summer some deals will fall into place and we'll be able to improve the squad again."
O'Donnell for Scotland?
Full-back Stephen O'Donnell made it a March double for Kilmarnock, picking up the player of the month prize.
With the right-back spot in the national team appearing to be up for grabs, his manager believes the 25-year-old could attract the attention of Scotland boss Alex McLeish.
"As far as international football goes it's always the same," said Clarke, who was capped six times while playing in the same position for Chelsea.
"If you do well for your club and are performing well for your club at a really consistent, high level then the international manager will have a look.
"I'm sure at some stage Alex McLeish will have a look at Stephen and see what he's doing and see if he can fit into his plans."