The Turnbull government has admitted it was aware former Family First senator Bob Day faced questions over his eligibility to serve in Parliament four weeks ago, but defended its decision to keep that information private until Tuesday afternoon.

It has emerged that questions arose back in August about Mr Day's eligibility due to a government lease, and that the government terminated Mr Day's lease last month.

Finance Minister Mathias Cormann said the government received independent legal advice last Thursday night that the lease may be in breach of section 44 of the constitution – rules that make it illegal for members of Parliament to receive ­"indirect pecuniary interests" from the Commonwealth.

The government handed that advice, centring on Mr Day's interest in the building where his Adelaide parliamentary office was located, to Senate president Stephen Parry on Friday morning, more than three days before Mr Day formalised his decision to quit the Senate and the controversy became public.