Both players were forced off during Sunday's 4-1 win against Aston Villa.
Postecoglou later said, "Yeah, I know Richy obviously felt something in the action of setting the goal up, his hamstring, so we'll see. Romero yeah, it was in that challenge again. He felt his foot was sore.
"I don't have any sort of further information. obviously, he's a pretty tough cookie for him to come off, it must be sore, but yeah, look it's not ideal. But again it's another game where we've had to reshuffle our back line.
"Radu (Dragusin) has played left centre-back, right centre-back, left centre-back, right-centre-back, Ben Davies has had to come in at different times and Destiny (Udogie) midweek and the boys are handling it really well. As I said it's not ideal but, hopefully both are not too serious."