We have only spoken of when the discussions may take place, says owner
The Reds boss was brought in as caretaker after Roy Hodgson's ill-fated reign came to an end, and was subsequently confirmed in the role until the end of this season.
And the improvement shown since the Scot's appointment coupled with being a fan favourite has seen him being touted for the job beyond the summer.
There had been reports claiming that the former Blackburn, Newcastle and Celtic boss had been offered a two-year deal to remain in charge at Anfield, but owner Henry insists that things have not progressed that far.
"The only discussion we’ve had has been with Kenny and that was solely concerning when we should begin discussions,” Henry told The Telegraph.
"I wouldn’t anticipate any further comments until such discussions have commenced and we have something to announce. Any reports until then are purely speculation."