"We are very flexible. Probably what you think we want, we don't. Maybe the things we want are the things you [Britain] will yield," he said.
"We do not want to run the lives of the islanders. If an agreement is found, I imagine the islanders would hardly notice."
Mr di Tella said he would suggest to the Foreign Secretary, Robin Cook, that they establish regular meetings at the Foreign Secretary's official residence at Chevening or elsewhere. A meeting with Mr Cook had been scheduled for next week; but it has been postponed due to the Foreign Secretary's busy diary.
The comments follow a meeting earlier this year between Mr di Tella and Malcolm Rifkind, the then Foreign Secretary, where diplomatic sources say the idea of dropping the Argentinian claim was discussed, but did not come to fruition.
"We had a very important meeting in Chevening in January," the Foreign Minister said in his first interview with a British newspaper since Labour's victory. "But it was very near the election so we didn't have time to spell out the positive consequences of that meeting. It was too short a meeting. I think they understood better our views and limitations, and vice versa.
"I hope we will be invited again to Chevening. I had also suggested to Mr [Malcolm] Rifkind [the former Foreign Secretary] that we have week- long meetings on a beach on a beautiful Caribbean island."
Contradicting recent Argentinian press reports, he said he did not foresee a major shift in Falklands policy by the Labour government and would not push Argentina's claim to sovereignty during his talks with Mr Cook. "My aspirations at the first meeting will be much more modest.
"We are fully aware that no British government will ever take a substantive decision on this issue without the approval of the islanders. The islanders have acquired a de facto veto. It's them we have to convince" of the benefits of contacts with Argentina.
However, the islanders are highly resistant to the idea of contacts, and they will hold elections to their legislative council later this year. But diplomatic sources say that they do not rule out some pressure from the Government in London on the Falklands to ease the ban on contacts with Argentina.
"I think we [Britain and Argentina] will reach a plateau relatively soon where we agree to disagree and we allow trade and communications [between Argentina and the islands].
"Britain invented this idea. You agree that disagreement exists and you shake hands. It's a non sequitur, it's just not logical to think that because we want tourists to go back and forth that we are talking about the issue of sovereignty," said Mr di Tella.
Aides to the Foreign Minister, however, later noted that he is acutely aware of not embarrassing the Labour government or giving the conservative opposition ammunition that could delay progress in efforts to reach a Falklands solution.
Press reports earlier this year saying Argentina expected more flexibility from a Labour government backfired from Argentina's point of view and brought a tough rebuttal from Tony Blair's government, the aides said.
"The change in government has meant no change whatsoever in policies. The only difference is that Labour has a majority of over 100 in parliament," Mr di Tella said. "In policies, we don't see any difference between the Conservative Party and the Labour Party.
"Some people in my country thought that a Labour government would be softer but they were thinking of the old Labour. The new Labour's policies are more similar to the Conservatives' than most people are aware. Kinnock's Labour may have made a difference but Mr Blair's Labour party is more similar to Conservative policies."
When he met the then shadow Foreign Secretary earlier this year, Mr Cook "made it clear, on this [Falklands sovereignty] issue, he would not change British policy. I said all I hope is that you continue British policy. We advanced quite a bit with the Conservatives."
The Foreign Minister said he hoped the Blair government would go ahead with John Major's invitation for the Argentinian President, Carlos Menem, to visit Britain officially for the first time, hopefully next year. "President Menem has visited every important country in the world except Britain," he said.
He also pressed for progress on the Falklands issue before 1999, when Mr Menem - barred from running again - will hand over to a new president. "There probably will be a continuation of the same policy but, if anything, the (Argentinian) line will be harder," he warned.
Mr di Tella described the new British Foreign Secretary as "very sharp, very intelligent, he goes very quickly to the point. I've met him twice before, the last time a month-and-a-half before the elections."
Mr di Tella, known for his so-called "Charm Offensive" of sending Christmas cards and other messages to the Falklanders, is considered aloof and arrogant even by Argentinians. He refused to accept that the Falkland Islanders can't stand him - "they're under peer pressure to say they dislike me but eventually they'll come to appreciate me" - and suggested the Union flag meant less to Britons or Falklanders than his own flag does to Argentinians.
He would not be drawn on Mr Menem's past remarks that the Argentinian flag would fly over the Falklands, even if alongside the Union flag, by 2000.
"This matter of flags. You can go in London and buy panties with the Union Jack. If you do that here with ours, you go to prison for lack of respect," he said, appearing to imply that seeing his flag over the islands would be more symbolic than significant.
Mr di Tella, Foreign Minister for the past six years, compared the lack of communication between Argentina and the islands with the situation between the Koreas or between Taiwan and China. "This position, unfortunately, doesn't give the islanders a good image. In a world where everybody wants to talk to everybody else, some people don't want to talk to a neighbour.
"It's difficult to hate for ever. It's very tiring and then you find you are very tired and you don't know why you hate. It's a bit pitiful, really." He described the islanders as "indeed part of the problem but a significant part of the solution".