Celustka has emerged as a target for Sunderland boss Paolo Di Canio after the Premier League club pulled out of a deal for Gino Peruzzi after the Velez Sarsfield full-back failed a medical.
Former Czech Republic Under 21 international Celustka has spent the past two years in Turkey with Trabzonspor after joining from Slavia Prague.
The 24-year-old, who has previously had a loan spell in Italy with Palermo, is expected to finalise his move to the Stadium of Light in the next couple of days.
Capable of playing at right-back, and in the centre of defence, Celustka was also linked with a loan move to Premier League new boys Crystal Palace.
He has also claimed he rejected a move to Trabzonspor's domestic rivals Antalyaspor in order to take up the chance to play in English football.
Celustka was quoted by the Daily Star Sunday as saying: "Antalyaspor wanted me, but my goal is to play in England."