The duo are among a number of players at Tynecastle who are out of contract at the end of the season.
Barr has been a regular this term following a slow start to his time at the club after arriving from Falkirk, while academy graduate Smith could not make a sustained first-team breakthrough despite scoring in an Edinburgh derby.
Another six players - defender Andy Webster, Marius Zaliukas, Danny Grainger, Dylan McGowan, and Fraser Mullen - have agreements which expire at the end of next month along with forward Arvydas Novikovas.
Hearts boss Gary Locke is uncertain on who will be staying at the club, but he insists his squad has much to play for.
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."