Gov. Norm Bangerter will meet briefly with President Reagan next week to discuss a plan to exchange land with the federal government at Lake Powell.

Bangerter hopes the land trade can be handled through Reagan, rather than through Congress.He requested the 15-minute meeting with Reagan and was notified Thursday the president will be available Tuesday.

The state wants to exchange lands within Capitol Reef National Park and Glen Canyon Recreation Area with federal lands on the shores of Lake Powell. Many visitors now traveling to the lake travel to Arizona because Utah has fewer points of access to the lake.

Bangerter also hopes to persuade Reagan to change the opinion of the National Park Service. The park service opposes the exchange and believes additional development would overcrowd the lake.

"There is more land in recreation areas than Congress authorized," he said.

Bangerter said the state has shortened the list of possible sites to three: Lone Rock/Wahweap Bay, the Bullfrog Bay Complex and Hall's Crossing.

Bangerter also wants to discuss highway trust funds that are being held from states or diverted to other programs.

He also wants Reagan to know of his desire for more latitude when dealing with the federal government.

"If they'd give me less guidelines and more latitude we could get better programs for the state," he said.

Bangerter said the state has serious transportation needs, particularly along the Wasatch Front. He defended the Utah Transit Authority's recent attempts to purchase land around a proposed site for a light rail system.

"I think it's prudent to make sure we have those rights of way," he said.

Bangerter will not meet with vice president and presidential candidate George Bush during the trip. However, he will meet with Bush during the Republican national convention, he said.

But, Bangerter said, he already has been asked for his opinion on who Bush should choose as a running mate. Bush supporters recently contacted all Republican governors for their opinions.

"I think he ought to pick a woman," he said, noting he thinks former transportation secretary Elizabeth Dole would be a good choice.

Bangerter and Reagan have planned a brief press conference at the White House on Tuesday afternoon.