Downing joined Middlesbrough from Premier League side West Ham on a four-year contract.
“The Spaniard has confided to friends that the club's former England winger Stewart Downing was not his signing and that he's finding it difficult to deal with the local hero and personal favourite of chairman Steve Gibson,” states the report in The Daily Mail.
Karanka did not take take training on Saturday morning and will not be in charge of Middlesbrough’s Championship game against Charlton Athletic away from home at The Valley on Sunday afternoon, as announced on the club’s official website.
It remains to be seen what happens with the former Real Madrid defender regarding his future at the Riverside Stadium.
Downing has scored three goals and created 57 chances in 34 Championship appearances for Boro so far this season.
The English attacking midfielder, who can also play as a winger, has a pass accuracy of 86% and a shot accuracy of 39%, and has won one header, seven dribbles and 19 tackles.