Karanka’s stance has changed from earlier this month when he said that there was no chance of Ramirez - a big-money target of champions Leicester City - leaving.
The Foxes remain keen on the 26-year-old and are set to reportedly offer £15m for the services of the ex-Hull City loanee.
Karanka said: “If the offer arrives and he wants to leave then we will consider it.”
Meanwhile, Karanka is calling on Jordan Rhodes to concentrate on football and put any transfer speculation to the back of his mind after Boro knocked two offers of £6m from unnamed Championship clubs for him.
Both fell short of Boro’s valuation, with Sheffield Wednesday reportedly one of the bidders along with Aston Villa.
Both offers were deemed below Boro’s valuation and were subsequently knocked back, and Rhodes’s future continues to be in doubt following the arrival of Patrick Bamford.
Karanka said: “I haven’t spoken with him, I don’t know what he knows but he is training and doing really well.
“That’s the main thing for him. He needs to forget about whatever is going on around him because if he is distracted he could get injured.
“The main thing is he is training really well and he is ready for whatever happens. If in two weeks the club has not received the right offers, then he will be still here.”
Hull City are being linked with Inter Milan defender Andrea Ranocchia, while Rotherham United interim-boss Paul Warne says that he values in-demand Danny Ward around the £5m mark.
QPR have seen bids of £1.2m and £1.5m for the Millers forward rejected with Eotherham having reportedly also received an offer of £2m from another Championship club.
Bradford City boss Stuart McCall has rubbished talk of a possible bid for left-back James Meredith.
The in-form defender, one of a number of players whose deals are up in the summer at Valley Parade, has been linked with Norwich and Leeds.
McCall stressed there had been no contact with the club.
He said: “We’ve had no offers for any of our players, so it’s pure speculation at this moment.”
Aston Villa manager Steve Bruce has expressed confidence that he can land Barnsley captain Conor Hourihane - and possibly wrap up the deal today.
National reports yesterday said that the Reds talisman was set for a medical in the Midlands after a fee had been agreed, but The Yorkshire Post understands that they were wide of the mark. But progress could be made today.