That is said to have infuriated Downing, who questioned whether the players could trust him after he walked out on the club last March following another training-ground row, only to return and lead the team to promotion.
Downing watched from the stands against City and there are fears he has played his last game under Karanka, who was willing to sell the winger last summer.
He was subsequently released without charges when it was proven that Downing was not in the Cross Keys Pub in Yarm, Teesside at the time of the reported assault.
“I am with them every day and on Friday, I will always choose at least 18 fighters.” However, Press Association Sport understands Downing, while growing increasingly frustrated with his lack of opportunities and concerned that he is shouldering a disproportionate share of the blame for Boro’s failings, has far from thrown in the towel and is determined to force his way back into contention.
Sources close to the player have insisted he has not downed tools and point to his confrontation with Karanka as evidence of his desire to help the club at which he made his name to drag itself out of relegation trouble.
The fact he would be on a free transfer makes the offer even more enticing as it would allow teams such as Brighton to afford to offer more competitive wages.
However, Downing could also choose to swap life at the Riverside for a transfer to the US, a move which almost fabricated in January.
This is something Downing has reportedly been interested in before so a move to Major League Soccer (MLS) would not be surprising.
If Downing preferred to remain in England, there are reportedly more clubs interested in the winger as well as Brighton, including Birmingham and Sunderland who would be looking to strengthen their sides in pursuit of Premier League football.
New Middlesbrough boss Garry Monk has been quick to stamp his authority at his new club, and has apparently made it clear that fan favourite and local boy Stewart Downing can leave the club.
Despite having two more years left on his contract, it's possible that the 32-year-old winger will look for a move away from the Riverside in the search for more first team football, The Northern Echo reported on Friday.
Downing has previously played for Liverpool, Aston Villa, Middlesbrough and Sunderland and has won the Football League Cup twice during his career thus far.