Henson, who currently plays for Bath, has been linked with a move back to his native Wales at the end of the season.
While the 32-year-old's future has yet to be decided, Jones insists that he will not be signing for Newport.
"I'm sure by Wednesday night you'll hear where he's going next year. Sadly not here," Jones is quoted as saying by BBC Sport.
Henson joined Bath from London Welsh in June 2013.