The ex-Liberal leader said he had told the former Prime Minister that a visit to extol the glories of the Union would be "very welcome".
However, he warned him not to campaign in Scotland if he planned to make a negative case.
Lord Steel, who served as Holyrood's first presiding officer, disclosed his words of advice during a debate on Scottish independence at St Columba's Church in central London.
Lord Steel said Sir John had asked him in recent days whether he should come to Scotland, as he has been asked to, to intervene in the referendum.
He said: "I said, 'Well, it is entirely a question of how you approach it. If you come north of the Border just to bash the Nats, that will be no good at all. If you come north of the Border as a former Prime Minister to talk about the glories of the Union and the contribution that Scotland has made to the Union historically and at present then that would be very welcome.'"
To a round of applause, he added: "I think that has got to be the tone of the campaign from now on, to talk about the contribution that Scotland has made and is making."
There is no suggestion the former Tory leader planned to do anything other than make a positive case.
Lord Steel's remarks come as the Coalition gears up for a new positive phase of the referendum campaign, as revealed by The Herald last week, which sources say will include an "injection of love" for Scotland.
The SNP have long accused the pro-Union parties of running overly negative arguments, criticising what they say is a Project Fear approach.
The Yes campaign received a boost yesterday as a poll showed support for Scotland breaking away from the rest of the UK had risen by four points in three months, to 42%, with 58% opposed after don't-knows were removed.
The findings also suggest Scots are increasingly sceptical about the suggestion that independence would leave their country as an economic basket case, despite Westminster's warnings over currency and interest rates.
Michelle Thomson, from Yes campaigners Business for Scotland, told the same London audience this week the arguments from the pro-Union campaign had been relentlessly negative.
She said: "I have yet to find anybody from the No campaign who can articulate a positive vision for the Union going forward. I hear what has been and I don't hear anything of what can be. This goes right to the heart of the debate; setting out what is the case for the people of Scotland, bearing in mind that change is necessary, change happens."
She received applause when she said that those campaigning for a Yes vote had set out a vision that was "forward and out, not inwards and back".
Last night a Better Together spokesman said: "Poll after poll shows people in the rest of the UK don't want Scotland to leave. Next month Eddie Izzard will be launching our Scotland, Please Don't Go campaign which will allow people in England, Wales and Northern Ireland to talk about the many positive reasons there are for keeping the UK together."
A Yes Scotland spokesman said: "The problem for the No campaign is that both its tone and content have been unremittingly negative, with no positive case to make. The UK is one of the most unequal countries in the developed world, with ridiculous decisions made at Westminster such as dumping a new generation of unwanted nuclear weapons in Scotland.
"The gap between Yes and No has halved since November, with new supporters for Yes such as former LibDem chief executive Andy Myles, and Lord Steel's comments indicate the concern clearly running through the ranks of the anti-independence campaign."