Mr Redwood, who once stood against then Prime Minister John Major for the party's leadership, also suggested there may have to be a new position created of First Minister of England.
The MP has called for an "English Parliament" to sit within the House of Commons if Scots vote against independence next month.
David Cameron's pledge that Scotland will have greater tax raising powers after a No vote has only made the case more urgent, he argues.
After a speech outlining the plans on Tuesday night, he said that what was needed was a "new voice" for England.
He added: "There there would be all sorts of consequential questions, which I don't want to make clear statements on tonight...
"Would there be a First Minister?
"Would there be any restrictions on MPs from other parts of the UK taking on roles within the English government?
"I think you would find that as soon as there was a body of English business, clearly defined English business, then there would be English voices."
John Reid, the former Labour MP for Airdrie and Shotts, served as Health Secretary between 2003 and 2005.
Advocates of a bar on Scottish MPs taking such a role argue that the jobs mainly deals with the English NHS.
But opponents warns that issues that affect Scotland, such as abortion law, come under its auspices.
Labour has warned that an "English Parliament" at Westminster would leave politicians who represent Scottish constituencies as "second class MPs".
The party has also questioned how easy it would be to identify "English-only" laws.
An analysis of data from the House of Commons Library by Tom Greatrex, the Labour MP for Rutherglen & Hamilton West, last year highlighted the difficulty identifying legislation which affects only England.
It found only a handful of Bills over the last 10 years would have been affected.
Even the often cited example of when Scottish MPs voted to increase university tuition fees south of the border was excluded, because that Bill contained provisions for Wales.
Mr Redwood said that he found arguments around what constitutes 'English only' laws a "bizarre question".
He said: "We already know and decide what is 'Scottish business' so is it not just the same thing?.
"It is just our business in England which they settle in Scotland".
The Tories, Liberal Democrats and Labour have all promised the Scottish Parliament would receive greater tax raising powers in the event of a No vote.
Before his speech Mr Redwood warned: "Many English people will not accept Scottish members of the Westminster Parliament voting through taxes on England that they do not have the power to impose on Scotland."
He suggests his proposals could be an answer to the long-standing 'West Lothian Question', a term first used by the former Labour MP for the constituency Tam Dalyell.
He asked how it could be right that he would be able to vote on policies that would affect Blackburn, in Lancashire but would not affect his constituents in Blackburn, West Lothian.