When asked on the BBC's Andrew Marr Show if he agreed with Johnson that the model is "crazy", Gove replied: "With the new customs partnership - Boris pointed out that because it's novel, because no model like this exists, there have to be significant questions marks over the deliverability of it on time".
The Brexit Secretary is to lead a new Cabinet group created to break the deadlock over future customs arrangements with the EU.
Mr Johnson's preferred model relies on technology to minimise customs checks. Foreign Secretary Boris Johnson branded the proposal "crazy" this week, saying in a Daily Mail interview that it amounted to "not taking back of your trade policy, not taking back control of your laws, not taking back control of your borders".
"It's totally untried and would make it very, very hard to do free trade deals", he told the Mail.
Gove, one of the leading Leave campaigners ahead of the 2016 referendum, said the result of that vote showed the British people want the United Kingdom to be free from the EU customs union.
The spokesman declined to say whether the PM had spoken privately with the Foreign Secretary about his comments.
The Prime Minister has set up the working groups after a meeting of the Brexit "war cabinet" failed to agree a way forward at a crunch meeting last week, sources have confirmed.
Mr Lidington acknowledged there had been internal criticisms of both models.
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For Prime Minister May, time is running out to heal the divisions in Cabinet.
Neither Johnson nor the chancellor, Philip Hammond, were included in the working groups, with cabinet sources suggesting that they were considered to be the "ultras" on each side, meaning their involvement could have made discussions hard.
May's preferred option, the customs partnership, was reportedly rejected at a meeting of her senior ministers last week, while Brussels has also condemned it as "magical thinking".
"The Prime Minister's plan would replace today's frictionless trade with a bureaucratic nightmare of tracking goods not just at the border but more or less anywhere and everywhere they are stored or distributed".
Environment Secretary Michael Gove, a leading pro-Brexit campaigner, said her customs partnership idea had "flaws", though he also acknowledged that neither plan was ideal.
The row came as Mrs May faces two more parliamentary defeats on her Brexit plan as it nears its final stages in the House of Lords.
"Now, I believe that now we have an implementation interval that provides us an extra 21 months after we go away the European Union to get every little thing proper".
Meanwhile, a further change has been proposed to the legislation that would require the Government to negotiate continued membership of the EEA.