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.
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.
Hearts boss Gary 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."