It would have to be demilitarised, he insisted. It would not be free to sign a military alliance with the likes of Iran or Iraq. The bottom line was: "I want a state, but I want it to be limited here and there."
Six months ago, Mr Bar-Illan would have denounced such views as heresy. He and his boss have learnt some hard lessons in office. If the interview reflects the Prime Minister's evolving position, it suggests that his government is coming to terms with the reality of a divided land, something which his Likud predecessors, Menachem Begin and Yitzhak Shamir, never did.
It suggests, however grudgingly, that Mr Netanyahu is braced to continue the Oslo peace programme, in deed as well as in rhetoric. Mr Arafat delayed signing a new deal on an Israeli redeployment from Hebron precisely because he feared the Prime Minister would then say: "Thus far and no farther."
Mr Bar-Illan was not providing a conclusive assurance. There will be hard and ugly bargaining to come, in the remaining stages of the Oslo II interim agreement, more Israeli evacuations, the freeing of Palestinian prisoners, the opening of "safe- passage" routes between Gaza and the West Bank, economic co-operation - and in the more traumatic negotiations for a final settlement of the Israeli- Palestinian conflict.
There are contrary signals, like the government's pledge to expand Jewish settlement on the West Bank and in the Arab neighbourhoods of East Jerusalem, though so far these are more talk than action.
But the interview was more than a straw in the wind. Mr Arafat looks like having something to bargain for.
Asked to define Mr Netanyahu's present ideological stand, Mr Bar-Illan told his interviewer that the Prime Minister was no longer a "whole-land- of-Israel" man. "I don't think he feels that there is any chance of the Land of Israel remaining completely under the exclusive rule of Israel," he said.
The next day, Mr Bar-Illan issued a statement distancing Mr Netanyahu from his aide's "private opinion". But the interview has not been repudiated, the chief of planning and communications is still at his post. Israeli commentators have noted, too, that Mr Netanyahu's right-wing Likud MPs have not yet demanded his head.
Until now Mr Bar-Illan, the former editor of the Jerusalem Post and a close friend of the Prime Minister, has always taken as hard and as pessimistic a line as Mr Netanyahu. The Arabs, and in particular the Palestinians, had not changed their spots - he thundered in dozens of editorials. Their strategic aim was still to kill Jews and destroy the Zionist state.
Aryeh Naor, a former Likud loyalist who served as cabinet secretary under Menachem Begin, then defected to Shimon Peres's peace camp, commented yesterday: "There seems to be an ideological revolution on the right as they are detaching themselves from the Greater-Israel ideology. If Bar-Illan talks this way, this tells you there is a new spirit of the times."
The signs are multiplying almost daily. The National Infrastructure Minister, Ariel Sharon, is backing the call for a national-unity government, or at least for a consensus of ideas, to negotiate a final settlement. The Israelis had to agree, the Likud maverick argued this week, on what they were prepared to give up and on what they would insist on keeping. Mr Sharon, the master settlement-builder of the Seventies and the Eighties, was talking territorial compromise.
At the same time, an informal group of Likud and Labour MPs, led by Michael Eitan and Yossi Beilin, has been meeting regularly to thrash out the terms of such a consensus. Mr Eitan is not a minister, but he is chairman of the coalition caucus. Mr Beilin, a candidate to succeed Mr Peres as Labour party leader, was one of the architects of the Oslo breakthrough.
Likud leaders, it seems, recognise that they cannot go back. They are committed, whether they like it or not, to completing the Oslo peace process. But they feel they can make the necessary painful concessions only with bipartisan support.
They need Labour and the left to outface their own messianic constituency, particularly among the West Bank settlers, who will have to pay the price.