His firm had held talks in recent weeks with senior MPs, Treasury and the Reserve Bank.
"We have been raising it and we've been getting interesting [raised] eyebrows. It's 'watch this space' I think."
Asked who had been briefed, he replied: "I would be talking to the Prime Minister."
Thompson said the scheme could be extended to people upgrading their family home, below the $600,000 price cap.
He admitted the cap would be tight in Auckland but said it would make some first-home buyers "downgrade" their price expectations, improving affordability.
His comments follow a period of sustained house price inflation that has seen Auckland's average house value tip $1 million.
With the Reserve Bank requiring most home buyers to raise deposits of at least 20 per cent, thousands of families have been locked out of the city's housing market, delayed having children or fled Auckland because of soaring housing costs.
In response, the Reserve Bank introduced new lending restrictions targeting investors last year, which have helped cool the market.
But Thompson said the loan to value ratio (LVR) rules were still too restrictive for entry-level buyers, forcing them to save huge deposits to qualify for mortgages.
"They slowed the market down and rightly so. They had to do that and I congratulate them on that. But now I believe it's time to give young people a helping hand."
Loan Market mortgage adviser Bruce Patten said Thompson's proposal had merit and would assist Kiwi families to purchase their first home.
But a $600,000 price cap would not help Auckland buyers, as there was little available in that range.
"My suggestion is that first-home buyers should be exempt if they have 10 per cent genuine saved deposit, haven't owned before and are in KiwiSaver."
A spokesman for Prime Minister Bill English referred questions to Finance Minister Steven Joyce.
Joyce told the Herald the Government had received no "recent approaches" from Barfoot & Thompson and the Reserve Bank was not "currently looking at this sort of proposal".
He noted that the LVR policy was now stricter for investors than for other homeowners.
"First-home buyers are often able to get a 'Welcome Home Loan' which is exempt from the LVR policy. Housing NZ's rules for this require only a 10 per cent deposit. The Government's KiwiSaver Homestart policy is also available for first-home buyers."
New Zealand Bankers' Association chief executive Karen Scott-Howman said banks were keen to help first-home buyers into properties, within the bounds of Reserve Bank lending restrictions.
They considered a customer's ability to service a loan, and affordability in case of interest rates rising or changes in personal circumstances.
"While we're not aware of this particular proposal, we're always interested in discussing options, and what the practical implications of any policy change might be."