Smith missed the 2-1 victory at Nottingham Forest last weekend due to bone bruising on his ankle and is currently in a protective boot, but Robins boss Lee Johnson says the midfielder will be tested in training on Friday.
Full-back Luke Ayling is in contention to feature for the first time since January following knee surgery.
Mark Little will also be available after being troubled by groin and foot injuries and Arnold Garita is making good progress from a knee operation, though the striker is not ready to feature this weekend.
Cardiff hope midfielder Peter Whittingham will be fit as the seventh-placed Bluebirds seek to bolster their play-off ambitions.
Whittingham missed last weekend's home victory over Preston with a calf strain but was in good form before that with four goals in five games.
Full-back Fabio da Silva also missed the Preston game with a groin problem but he is less likely to return with the midweek visit of Leeds a more realistic target.
Sean Morrison (knee) and Craig Noone (chest) are both nearing full fitness after long absences, though the pair may have to be patient to rejoin Russell Slade's matchday squad.
MATCH FACTS
- There have been 18 goals in the last four meetings between these sides at Ashton Gate (8 for Bristol City, 10 for Cardiff).
- Cardiff have won six of their last nine games against the Robins in all competitions (D1 L2).
- The Robins have won four of the five league games, losing their last home game 4-0 to Brighton.
- The Bluebirds lost their last away match 3-1 at Middlesbrough, their only defeat in their last eight league outings (W4 D3).
- No Championship side has seen fewer players score a league goal for them this season than Bristol City (10).
- Anthony Pilkington has scored eight league goals this season, his best return since 2011-12 (eight goals for Norwich).
Referee: Graham Scott