City manager Gary Johnson was present at Rugby Park on Sunday as Naismith's penalty was enough to beat Hearts.
And BBC Sport believes that the Scotland Under-21 striker and Pospisil were the men he was checking out.
Pospisil turned down a move to City in January after the two clubs agreed a £100,000 transfer fee for the Czech.
He preferred to stay at Tynecastle to battle for a first-team place.
But Johnson's side have since won promotion to the Championship and will hope that playing in England's second-top league would be enough to persuade Pospisil to move in the summer.
Pospisil has been troubled with injuries this season but was a starter in Hearts' final two league games of the season.
Johnson would face greater competition for the signature of Naismith.
Rangers are definitely interested, while Aston Villa manager Martin O'Neill was also at Rugby Park on Sunday.
But Kilmarnock are likely to demand at least £1.5m for the 20-year-old.
BBC Sport