Boro have already had one bid rejected by Blackburn for Rhodes, who scored 21 goals in the Championship last season, and reports suggest they could return with a new offer but Karanka was remaining tight-lipped about his club's interest in then Scotland striker.
"I don't want to speak about Jordan Rhodes every press conference because he is not my player and I have to think about my players."
Karanka added: "We need players who will score goals. We have Kike and (Christian) Stuani and we need to bring in players who can score goals.
"Jordan is one name on the list and we have other ones. We have to make sure we get the right ones."