Do you want Vice President Dick Cheney’s undivided attention for an hour? Stephen P. Payne, a Texas-based lobbyist, has some advice about how to grease the wheels for such a meeting: Make a six-figure donation to the George W. Bush Presidential Center, a library and museum complex that is scheduled to be built at Southern Methodist University.

When Mr. Payne made that suggestion in a London restaurant last week, he thought he was talking to an agent of the exiled president of Kyrgyzstan. He was actually speaking with undercover representatives of The Times of London, which has posted a video of the encounter.

“I think that the [exiled president’s] family, children, whatever, should probably look at making a contribution to the Bush library,” Mr. Payne says in the video. “How big, I don’t know. It would be like maybe a couple of hundred thousand dollars, something like that. Not a huge amount, but enough to show that they’re serious.”

Mr. Payne, a member of the U.S. Department of Homeland Security’s Secure Borders and Open Doors Advisory Committee, runs a Houston lobbying firm called Worldwide Strategic Partners. He has no affiliation with the George W. Bush Presidential Library Foundation or with Southern Methodist. In a statement released on Sunday, Mr. Payne argues that he was entrapped by the Times agents’ “bizarre leading questions and strange hypothetical comments.”

The controversy arrives just days before critics of the Bush library are planning a last-ditch effort against the project. Later this week, delegates to the annual meeting of the United Methodist Church’s South Central Jurisdiction, which owns SMU, are expected to vote on a resolution that would withdraw the church’s approval for the library.

The effects of such a vote are not certain. The university maintains that it won full and final approval for the library last year from a different church body, known as the Mission Council. If this week’s resolution passes, the dispute might be sent to the church’s national Judicial Council.

Critics of the presidential-library system have long warned that anonymous donations to presidential foundations can lead to bribery, or the appearance thereof, especially when the president has not yet left office. In 2001, Time reported that the songwriter Denise Rich had donated approximately $400,000 to President Bill Clinton’s library foundation at around the same time that he pardoned her fugitive husband, the financier Marc Rich. And this year The New York Times investigated Mr. Clinton’s relationship with a Canadian mining magnate who had donated heavily to the foundation after using Mr. Clinton to win the good graces of the president of Kazakhstan.

Last year the U.S. House of Representatives overwhelmingly passed a bill that would require transparency in donations to presidential libraries. There has been no Senate vote because Sen. Ted Stevens, a Republican of Alaska, has placed a hold on the measure.

The Bush foundation and SMU have not yet begun a formal fund-raising campaign for the Bush center, which is expected to cost up to $500-million. But they expect to start raising funds well before Mr. Bush leaves office, according to news reports. (University officials did not reply to The Chronicle’s inquiries today.)

The master agreement between SMU and the Bush foundation contains a provision (beginning on Page 115) that requires the university to work heavily on the fund-raising effort. After $200-million has been raised, 15 percent of any additional funds would be given to the university to support academic projects related to the presidential center. —David Glenn