Hibernian could condemn Hearts to relegation in the Edinburgh derby on Sunday, ending their city rivals' 33-year stay in the Scottish top flight.
If second bottom St Mirren pick up a point against Inverness Caledonian Thistle on Saturday then Hibs can send Gary Locke's side crashing into the second-tier Championship with victory at Tynecastle.
Hearts remain in administration but Locke insists it is the 15 points penalty and transfer restrictions imposed on him at the beginning of the season which has done the damage to their on-field ambitions.
"I'm a realist and a lot of the Hearts fans are realistic too. They understand the situation and the most important thing is that the club is still here," the Hearts boss said.
"We will all be disappointed if we are relegated. We are all realistic enough to know avoiding it is a near-impossible task now.
"But there has been circumstances which have contributed to our struggles. We have a depleted side with young players and we had to start the season minus 15 points.
"It's not been ideal but there has been a lot of positives to take out of this season. I can look to the progress a lot of younger players have made and hopefully that will stand us in good stead for the future.
"People keep going on about the fact Hibs can put us down. But it's not Hibs who will do that. We've had the 15-point deduction and that has been a big ask to overcome, especially with the youthfulness of the squad.
"It's not one game that will relegate us. It's the fact that over the season we have not been able to claw back that 15 points."
Meanwhile, Anthony Stokes insists Celtic won't ease up despite clinching their 45th Scottish league title in record time.
The Hoops sealed their third successive Scottish Premiership championship following an emphatic 5-1 win over Partick Thistle at Firhill for the earliest top flight title victory since 1928/29.
The Glasgow giants have dropped just nine points on their relentless march to the title, tasting defeat just once in a season where goalkeeper Fraser Forster set a new Scottish shut-out record of 1,256 minutes.
The Celtic players were denied a proper party after Wednesday's match at Firhill following a pitch invasion by fans but will be able to perform a lap of honour at Saturday's home game against Ross County.
And despite sealing the league crown, Stokes says the players won't be tempted to drop their performance levels.
"It will be nice to celebrate at home in front of our fans," said Stokes.
"It wasn't ideal with the way things turned out at Firhill but sometimes the occasion just takes over and you can't have too many complaints.
"We don't want to tail off. We want to go and try and impress them every game, and that won't be any different from now until the end of season. The fans pay good money to come and see us play and they deserve us to put on a show for them.
"I want to score more goals, keep playing the way I am, try and be as consistent as possible and try and help the team."
Aberdeen v Dundee United, Celtic v Ross County, Inverness CT v St Mirren, Motherwell v Kilmarnock, St Johnstone v Partick Thistle
Hearts v Hibs