With David Wheater and Gary O'Neil having left the Riverside, Boyd is the final member of the high-earning triumvirate that Middlesbrough manager Tony Mowbray was hoping to move on this month.
Boro are willing to let the Scotland international leave on loan in order to reduce their wage bill, and there have been expressions of interest from two leading Turkish clubs.
The strongest approach, however, has come from Russian Premier League side Terek Grozny, who recently appointed former Newcastle United manager Ruud Gullit as their new head coach.
Gullit has been given a significant transfer kitty to spend this month, and had targeted Boyd as a potential marquee signing.
Grozny are understood to be willing to pay Boyd more than the reported £35,000-a-week he is earning at Middlesbrough, but the 27-year-old has no interest in a move to the capital of Chechnya.
A return to his former home at Ibrox would make more appeal, but having inquired about Boyd's possible availability on a number of occasions this month, Rangers boss Walter Smith has accepted he will be unable to match his current earnings at Boro.
Boyd left the reigning Scottish Premier League champions as a free agent last summer, and secured a substantial pay increase when he signed on the dotted line at the Riverside.
"It's a simple one, that one," said Smith, when asked about Boyd's situation at a press conference in Glasgow yesterday. "We couldn't afford to pay the money that Middlesbrough were paying last season and we are still in that position where we cant afford to pay it now.
"It's just a situation where Kris left us to go to a club who could pay him more money. We couldn't pay him that money and we still can't, and that's the situation.
As well as looking to move more players out of the club, Mowbray is also hoping to make a couple of additions to his squad before the transfer window closes next Monday."
Bayern Munich reserves skipper Maximilian Haas is a leading target, but there is no chance of fellow German Anis Ben Hatira, mentioned as a possible replacement for O'Neil, moving to Teesside.
Ben Hatira, a Germany Under-21 international, has recently broken into the Hamburg first team, and while Boro scouts watched him earlier this season, a transfer this month is unlikely.
Boro's hopes of securing Andrew Davies also receded yesterday when Stoke City recalled the defender to the Britannia Stadium.
Mowbray had been hoping to field Stockton-born Davies, who has been training with Boro for more than a month, in tomorrow's reserves game with Hartlepool United.
However, with an agreement over Davies possible transfer not forthcoming, Stoke boss Tony Pulis has opted to recall the defender, even though he has little chance of featuring in the Potters first team.
Further talks are likely in the final five days of the window, but the financial practicalities of terminating Davies' Stoke contract and agreeing a new deal on Teesside are proving problematic.
One contractual situation did get resolved yesterday, with highly-rated left-back Joe Bennett signing a new four-and-a-half year deal with Boro.
Bennett, who has started Boro's last 13 league games, is the fourth Academy product to sign an extended deal in recent weeks, after Jason Steele, Cameron Park and Connor Ripley also put pen to paper.
"I can't speak highly enough of Joe," said Mowbray. "He is technically very gifted, he is mobile, fast and he can cross a good ball from out wide.
"Although he is quite slight, he is tenacious and he doesn't hesitate to go in for a 50-50 ball. He has all the qualities to become a Premier League footballer. Hopefully, we can achieve that target together.
"Having said all that, he is still only a boy of 20 and he will make some bad decisions at times, but I am sure he will keep improving. What he's got to do now is get his head down, work hard and keep doing what he's doing."
O'Neil was formally confirmed as a West Ham player yesterday morning, and could be involved in this evening's Carling Cup semi-final second-leg tie with Birmingham City.
"I enjoyed my time at Middlesbrough," said O'Neil. "The fans and staff were really good, but it has been a difficult time on the pitch. It's nice to be back in the Premier League and play at the top level, which everyone wants to do.
"I am London born, so it is good to come home. It all happened very quickly. I played for Middlesbrough at the weekend and didn't know anything was going to happen, but it has all gathered pace since then."
* Middlesbrough will face Nottingham Forest in the fifth round of the FA Youth Cup after Charlie Wykes goal secured a 1-0 win over Everton.
Source: Northern Echo
Source: Northern Echo