The 19-year-old has made 23 appearances since joining on loan from Chelsea in the summer.
There had been suggestions that Chelsea may invoke their right to recall McEachran, who suffered a recurrence of an ankle injury against Blackburn on Boxing Day.
But Mowbray told local radio: "I've had conversations with some of the Chelsea hierarchy and they're 99.9% sure he won't be recalled in January.
"Unless they have a catastrophe with injuries, I think Josh will be staying with us until the end of the season."
McEachran has made 22 appearances for Chelsea and played five games during a loan spell at Swansea City last season.
Middlesbrough sit fourth in the Championship and are two points off an automatic promotion place.