Ex-England midfielder was left out of starting line-up for their win at Wolves on Saturday.
The Spaniard clashed with the big-money summer signing after the recent draw with Fulham and loss to Cardiff.
The Sunday Mirror confirms that things came to a head in midweek and that that led to Downing being left out of the side that started at Molineux.
However, with Boro losing 1-0, Downing was introduced just after the hour mark and made a huge impact - creating the equaliser, setting up the penalty for the second goal and curling home a brilliant free-kick in injury time to seal the win.
Downing admitted after the game he was not happy to be left out and told the Evening Gazette: "I’m not going to stand here and lie, I was very disappointed not to start the game.
"Like every other player I came here to play, I want to play every minute from a selfish point of view.
"I know that’s not going to happen all the time, but the only way to respond is to perform. There’s no point moaning about it or sulking, you do the talking on the pitch."
But HITC Sport understands that a host of Premier League clubs have already been alerted to the possibility that they could prise Downing away from Boro in January - if the differences between him and Karanka are not ironed out.
New Sunderland boss Sam Allardyce is a huge fan of Downing and got the best out of him at West Ham last season, which saw the midfielder recalled to the England squad.
And Allardyce will have no qualms about trying to grab the 31-year-old if he thinks a deal can be done - but Boro, one of the promotion favourites, are unlikely to be willing to do business with Sunderland unless they have to.