The pair are among a number of players who are out of contract in the summer.
Barr has been a regular over the past 12 months following a slow start to his Tynecastle career after arriving from Falkirk, while academy graduate Smith could not make a sustained first-team breakthrough despite scoring in an Edinburgh derby.
Hearts boss Gary Locke earlier encouraged his team to land as many points as possible in their five remaining games and net the club a much-needed windfall.
The Tynecastle outfit currently sit 10th in the Clydesdale Bank Premier League, five points behind seventh-placed Kilmarnock, who they play at Rugby Park on Saturday.
But the performance of the club's finances this season have been just as concerning for the Gorgie faithful as their team's on-field displays.
In December, the club had to appeal to their supporters through a share issue after Her Majesty's Revenue and Customs handed them a winding up order over a £1.75million unpaid tax bill.
But finishing seventh will net the club around £300,000 more in prize money than is dished out to the team limping home in 11th place and now Locke has pleaded with his players to do the club a financial favour and bring home the money.
He said: "The difference between finishing seventh or lower can be massive. Everybody knows the position the club is in financially.
"We are not out of the woods by any means and the higher up the league we finish, the more we can help the club.
"It's great that we have another Edinburgh derby to look forward to and that will help as well. But to finish as high up as we can will not only boost the pride of the players and myself, but the club's finances as well."
And Locke also suggested it is not just the club's future that is at stake, warning new deals for out-of-contract players must be earned between now and the end of the season.
Another six players - Andy Webster, Marius Zaliukas, Danny Grainger, Dylan McGowan, Arvydas Novikovas, and Fraser Mullen - have agreements which expire at the end of next month.
Locke said: "We are still not sure what is happening but no matter what, players are playing for their futures here or for their futures somewhere else.
"It's important that they give it their all from now until the end of the season.
"I know the lads really well and no matter who plays, they will give it everything they have got. Hopefully that will be enough to get us some victories."