"Now is not the right time to outline long-term plans," the Treasury says.
The chancellor will give an update on Thursday about "protecting jobs" as the furlough scheme winds down.
But the Labour leader says another "divisive" vote on Scotland's position in the near future is "not needed".
The government plans to create an internal border to prevent gridlock on the county's motorways.
Chris Whitty and Sir Patrick Vallance were alarmed by questions over the controversial concept, emails show.