With a grin of sheer delight, Mr Sharon brushes dust off a brown envelope, tugging out dog-eared maps. His chubby fingers lovingly finger what Palestinians call the Israeli-occupied West Bank, but Mr Sharon calls Judea and Samaria - the land of 'Eretz Israel', which he, and other ultra-nationalists, believe stretches from the Jordan river to the Mediterranean. Mr Sharon, 65, then raises his large bulk over the desk to point out six amoeba-like shapes, superimposed on Judea and Samaria. These, he says, would be 'cantons', inside which all Palestinians in the area would be forced to live, surrounded by checkpoints on every access road.
The area of Gaza is also lopped into three by amoeba shapes. 'It is hard to establish a state when you have these sub-districts,' he says. The separate ghettoes would ensure there could be no freedom of movement for Palestinians. Meanwhile, the 130,000 Jewish settlers in the occupied territories would travel unimpeded, under 'Israeli sovereignty'. It is, explains Mr Sharon, 'Palestinians who kill Jews - Jews don't kill Palestinians'. He adds enigmatically: 'We don't want Jewish ladies being searched by Palestinians.'
Mr Sharon's proposal is an old idea for solving the Palestinian question. Significantly, however, it is being revived by the former Likud defence and housing minister, just as the Israeli government's plan for interim Palestinian self- rule is beginning to take shape. The Labour-led coalition, headed by Yitzhak Rabin, the Prime Minister, is proposing self-rule over a proportion of the West Bank and Gaza Strip, excluding Jewish settlements and Jerusalem.
In the absence of any effective opposition to Mr Rabin from Benjamin Netanyahu, the Likud leader, Ariel Sharon has launched a new offensive, fuelling strong rumours that he may seek to exploit disillusionment with Mr Netanyahu - and take advantage of a slowing momentum for peace - by challenging for the Likud leadership. 'It may happen,' he says, cryptically.
Whatever Mr Sharon's real motives his cantons plan is the only substantive opposition alternative to the self-rule deal. He has even discussed it in private meetings with Mr Rabin. 'I want the government to be aware of all the dangers of autonomy,' he says. These talks have led to further rumours of a new alliance with Mr Rabin, but the meetings are more likely to signal the pleasure two old generals take in discussing battlefield ideas.
The question is: can Mr Sharon win the power and influence to undermine self-rule and promote cantons? Few political analysts believe Mr Sharon is likely to rise to the top of the post-Shamir Likud. The 'young princes' - as the Likud young generation are known - distrust Mr Sharon. Even on the right his Lebanon venture of the early Eighties, which led to the most unpopular and divisive war in the country's history, is widely viewed as reckless.
In his office, Mr Sharon's talk of 'Arafat the war criminal' and his description of the house he provocatively bought in the Muslim quarter of the Old City as a 'forward position' seem discordant in the new era of peace.
Nevertheless, there are plausible scenarios that could put Mr Sharon's ideas - if not the man himself - back in the limelight. It remains conceivable the still fragile plans for Palestinian self-rule could disintegrate, ultimately damaging Mr Rabin. Jewish settlers are constantly looking for new allies in Jerusalem power centres - and nobody has promoted their cause in the past like Mr Sharon, who backed the building of many of the settlements. Even if the autonomy deal is a success, there is no guarantee that Labour would win the next election say some political observers.