The Canaries have made an approach for the former Carrow Road midfielder and want to name him as assistant to manager Neil Adams.
But it appears the Bairns jumped the gun when they posted a statement on their official website claiming he had officially left the Scottish Championship.
In a fresh statement, they now claim Holt remains head coach at the Falkirk Stadium for the time being.
The statement read: "Falkirk Football Club would like to apologise for the previous incorrect posting on this website.
"The Club has given Norwich City permission to speak to our Head Coach, Gary Holt. At this time, there is no update to that position and the club confirms that it has not received any formal communication regarding these talks. Gary Holt remains the club's Head Coach until formal agreement is received."
Earlier on Monday afternoon, the club had announced it had accepted Norwich's offer for Holt, who spent four years as a player with the Sky Bet Championship side and worked with Adams in the club's academy set-up before being named Falkirk boss last year.
It said: "The club can confirm that Head Coach Gary Holt has accepted a coaching role at Norwich City after Falkirk granted the Carrow Road side permission to speak to him over the weekend."
Bairns chairman Martin Ritchie added: "The Club fully understands Gary's wishes to return with his family to Norwich. We would like to wish him every success in the future and to thank him for all his work at Falkirk over the last year."
Holt led Falkirk to third in the Scottish Championship this season but lost out on promotion when they were beaten by Hamilton in the play-off semi-finals.
But his employers had even started the search for his replacement, adding in a further statement: "Following today's announcement that Gary Holt is leaving the club to take up the post of assistant manager at Norwich City, the search starts immediately for a new head coach.
"The club aims to have a new head coach in position by the time the team come back for pre-season training on Thursday, June 26. To meet this very tight timescale, the club will draw up a shortlist of potential candidates by the end of this week."
Ritchie was unavailable for further comment.