The Independent has learnt that the approach was made to Mr Trimble by a member of the Rev Ian Paisley's Democratic Unionist Party. It is unclear whether the go-between was operating with Mr Paisley's knowledge.
Mr Trimble said at the weekend that unity between his party and Mr Paisley's more extreme DUP was his objective and would come possibly sooner than people realised.
The best way of reflecting Unionist unity, he said, was with a single united Unionist party under the leadership of whoever that party selected as leader. That was his objective, Mr Trimble said.
Mr Paisley yesterday signalled his reluctance to see a merger while he remains DUP leader, but he did not rule it out.
"I don't think that there is going to be a merger of the two parties. I think there will be a closer working together if we all come together in the Unionist Convention. Who knows what lies ahead after that?" he said.
Mr Paisley, who was flying to America, said Mr Trimble had "outsmarted the other contenders in a very much divided party" to become UUP leader.
The tentative moves towards Unionist unity came as the most senior civil servants in the Irish and British governments met in London to seek a way through the impasse over decommissioning of IRA arms.
Sir Robin Butler, the Cabinet Secretary, met Paddy Teahon, the permanent secretary to the Taoiseach, John Bruton, to find common ground to reconvene the postponed summit between the Prime Minister, John Major, and Mr Bruton.
They were hopeful of reviving the idea of an international commission, in spite of Sinn Fein objections which caused the summit to be postponed by the Irish government last week.
Gerry Adams, the Sinn Fein president, before heading for Washington, denied a New York Times report he had softened his opposition to the commission.
"The commission idea had been scuppered by the British government, by John Major and by Patrick Mayhew some weeks ago when they insisted it was really a collection agency for their demand of an IRA surrender of arms," Mr Adams said on Irish radio.
"That report is totally inaccurate," he said. "Sinn Fein doesn't have any room to manoeuvre. Sinn Fein has a willingness to be involved in all- party talks. We want to bring nothing more than our mandate to those negotiations."
Mr Adams will meet the US national security adviser, Anthony Lake, during his five-day trip in an effort to get the US to put pressure on Mr Major to drop his demand for IRA arms decommissioning in advance of all-party talks.
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