King Hussein of Jordan, in a prelude to a White House meeting with President Reagan today, conferred with Secretary of State George P. Shultz for more than two hours yesterday and said afterward that the talks had left him "very hopeful" about prospects for Mideast peace.

Hussein did not elaborate, but U.S. officials have said that the king's main purpose in his visit here is to seek assurances that Reagan is determined to pursue his Mideast peace initiative with its long-range goal of giving Israeli-occupied Arab territories eventual independence "in association with Jordan."

U.S. officials have cautioned that they do not expect any breakthroughs from Hussein's visit.

However, U.S. policy makers say they believe Hussein wants to enter a broadened peace process similar to that outlined in the Reagan initiative. They also are hopeful that the talks here will encourage the king and buttress his negotiations with other Arab governments and the Palestine Liberation Organization.

The immediate U.S. hope is that the intricate, ongoing talks within the Arab world will result in the PLO and moderate Arab states giving Hussein a mandate to enter the talks over autonomy for the West Bank and Gaza Strip as the representative of Palestinian inhabitants of those territories.

In the U.S. view, if Hussein can be induced to enter the talks, Israel, despite its rejection of the Reagan initiative, will have no choice other than to respond positively. The administration then would have achieved its first-stage objective of bringing about a reactivated and broadened peace process.

Hussein's visit also is expected to result in a formal U.S. offer to sell Jordan two squadrons of F20 jet fighters and a quantity of shoulder-fired Stinger antiaircraft missiles. However, that will only partially satisfy Hussein, who wants the more sophisticated F16 fighter-bomber and the mobile ground-to-air Hawk missiles even more.

U.S. sources have said that congressional objections and the unsettled situation in the Middle East preclude a decision on this additional weaponry at present.

Although the administration has hinted that movement toward Mideast peace could lead to a favorable decision, it is not clear whether Hussein will regard the U.S. offer as sufficient to smooth over the sensitivity in relations between the countries resulting from Jordan's arms requests.

In a related development, Reagan's special Mideast representative, Philip C. Habib, was scheduled to arrive here last night from Israel, where the government announced Sunday that it had dropped its demand that talks on withdrawal from Lebanon be held in Jerusalem.

Habib will brief Reagan this morning on the prospects for Israeli-Lebanese negotiations on withdrawal. He also will participate in Reagan's meeting with Hussein.