Karanka said that he has been given Chelsea's permission and is now just waiting on Bamford to commit to the deal.
"I hope Patrick will be with us as soon as possible but it's not in my hands," Karanka told the club website.
"I've spoken with him and given him my trust that I believe he can be a very good player for us because we only have Kike as a striker at the minute.
"At the moment it's up to him. I've spoken to Jose [Mourinho] and Chelsea are happy for him to come, we want him so hopefully we can persuade him to come and have him as our player."
Bamford, 20, scored eight goals in 23 appearances during a loan spell with Derby County during the second half of last season.