The Boro boss has maintained close ties with Chelsea coach Jose Mourinho since working with him at Real Madrid, but has also held discussions with other top-flight teams.
"We are working until the last day [of the transfer window] because at the minute we haven't got the squad we want, but I'm happy with the performances of the players I have now," Karanka told the Evening Gazette.
"We are working not just with Chelsea, but with other big teams in the Premier League. Our link with Chelsea is good because everyone knows my relationship with Jose, but it's not just with him.
"I would like to finish [transfer business] before the deadline but sometimes you have to wait until the last second. I want to finish this transfer window with all the players I wanted two or three months ago. If we do that I'll be very happy."
Karanka recently expressed interest in taking Chelsea striker Patrick Bamford out on loan.