The Championship side have been heavily linked with the English frontman, but after witnessing his team lose 1-0 at Leeds United, Karanka admitted that he was not sure whether they would be able to bring the 20-year-old to the Riverside Stadium.
The Spaniard told reporters: "We are working on Bamford. I have spoken with Jose Mourinho, everybody knows how important a player he could be for us.
"I hope that he can be with us but it is not in my hands. We would like to have a squad with a lot of quality so there is competition for the players."
Bamford scored eight goals in 23 appearances during a loan spell with Derby County during the second half of last season.