Police investigating alleged abuses of the honours system have refused to comment on reports they are preparing to interview Labour party donors.
Mr Smith was the subject of a newspaper investigation (Photo: Sunday Times)
A head teacher arrested as part of the cash for honours probe was freed on bail on Thursday after questioning.
Des Smith, 60, quit the City Academies programme after a paper accused him of promising honours to people who sponsored the institutions.
Mr Smith is expected to release a statement through lawyers after Easter.
The cash-for-honours inquiry was originally launched in response to a complaint by Scottish and Welsh nationalist MPs that Labour had broken the law preventing the sale of honours such as peerages and knighthoods.
Labour went on to reveal it had been secretly loaned nearly £14m ahead of the last election. The Conservatives were loaned a total of £16m by 13 wealthy backers.
The inquiry has since been widened to cover the activities of other parties.
Deputy Assistant Commissioner John Yates, who is leading the police investigation, has said he is prepared to consider more general allegations of corruption.
Mr Smith had already resigned from his post with the Specialist Schools and Academies Trust.
He was freed on bail on Friday after being held for questioning under the 1925 Honours (Prevention of Abuses) Act.
In January, he had suggested sponsors for the government's flagship city academies programme would be given honours in exchange for funding.
The trust helps the government recruit education sponsors. Set up in September 2005, its president is Lord Levy, Tony Blair's chief political fundraiser and close friend.
Mr Smith, who remains headmaster of the All Saints Catholic School and Technology College, Barking and Dagenham, quit his post on the SSAT council in January after admitting he had been "naive" when talking to a reporter posing as a potential donor's PR assistant.
He reportedly told the Sunday Times that "the prime minister's office would recommend someone like [the donor] for an OBE, a CBE or a knighthood".
Downing Street said at the time it was "nonsense to suggest that honours are awarded for giving money to an academy".
Education select committee chairman Barry Sheerman insisted there is no link between sponsoring specialist schools and receiving political honours.
He told BBC Radio 4's Today programme: "All politicians are lobbied constantly from friends and supporters of people they think deserve an honour, whether it is an OBE, a CBE, a knighthood or a peerage.
"We have a tradition in this country that people who get these things are the sort of people who have given back in various ways. And, of course, the system is pretty imperfect."
Code of conduct
He said he very much doubted that "any senior politician would get involved in saying 'if you do this, you will get this sort of honour' ".
Labour MP David Chaytor MP, also a member of the education select committee, told Radio 4's The World at One programme he feared the latest allegations raised questions about city academies.
"What we have here with the SSAT is almost a Department for Education and Skills outside the Department for Education and Skills, and that raises all kinds of questions of accountability."
In a separate development, elections watchdog the Electoral Commission has published a new draft code of conduct on reporting loans.
It says the parties agree to report any loan more than £5,000 - or more than £1,000 if the donor has given another amount that needed to be reported in that year.
Anyone found guilty under the 1925 Honours (Prevention of Abuses) Act - designed to deal with those who both give and accept honours under inducement - could face imprisonment for up to two years or fined an unlimited amount.