Once that is achieved, he reckons the fact the club's remaining games of the season will all be against sides in the upper echelons means there is every chance of breaking into the top four.
"I'm looking to get in top six as quickly as possible," said Jefferies, whose side were both eight points clear of seventh-placed Aberdeen and eight behind third-placed Dundee United ahead of Sunday's trip to Tannadice.
"Teams are catchable above us with the games that are left, and if you get in the top six, you've got them to play again.
"There are teams above us we've got to play twice if we stay in the top six, so there is room to go and challenge.
"But, first and foremost, it'll be getting in the top six and then we'll take it from there."
Striker Elliot, who is a month into his latest comeback from the knee surgery which has kept him out for most of the season, knows the importance of the next three matches.
After Sunday's clash with United, Hearts travel to Motherwell before the third Edinburgh derby of the season against Hibernian.
"We've obviously got a massive game on Sunday and I think if we were to take three points from that, we'd start looking above," he said.
"At the moment, it's kind of difficult to look three or four games ahead when we've got three massive games in front of us.
"We're just taking it one game at a time and we've got to try to concentrate on getting three points on Sunday.
"After that, we'll look at the teams ahead of us."
Jefferies is more than a month into his second spell in charge at Tynecastle.
After a sticky start, he has got Hearts' season firmly back on track and, following last weekend's 1-0 victory at Aberdeen, they are looking for a fourth win in a row for the first time since November 2008.
"Each day that's gone by has got better because we've got to know the players," said Jefferies, who has managed a hat-trick of victories despite one of the worst injury crises of his career.
"Once everybody's fit and well, you've got competition for places and it gives me more options to decide from.
"The one thing the players have done is responded to what we're looking for.
"You could see that was evident last week when we had to do all these things during a game to get a result against a team that's beaten us twice recently."
Hearts could be without as many as 14 first-team squad members tomorrow through injury and suspension.
Jefferies said: "We may have to go and grind out and chop and change and people will just have to expect that.
"We'll not be at our strongest.
"The players pulled together last week; they'll have to do the same this week to get a result.
"Let's be honest, Dundee United are more consistent than Aberdeen this year and it'll be a tough game."
Dundee Utd 5/6, Draw 23/10, Hearts 7/2
Source: Team Talk
Source: Team Talk