No. There was no serious attempt to propose a specific surrender agreement to the US or Allies as a whole. No Japanese official explicitly approached either the US or any intermediary with any surrender plan. Here's a basic summary of what the surrender negotiations were between April and August.

Sweden - There were two attempts to use Sweden as a go between. One started between Widar Bagge (minister to Japan) and Mamoru Shigemitsu (former foreign secretary). But these were unofficial talks and Shignori Togo stomped them out, because he didn't want to use Sweden, hoping for a more prestigious go between. The second attempt was by Sweden's Prince Carl who approached Makoto Onodera, an attaché in Stockholm. Onodera received back a cable that said "Japan's policy is to fight to the end." He also received instructions to investigate anyone attempting to conduct "peace moves." He wasn't provided any instructions for supporting such moves if he found them, but personally interpreted it to mean that he was supposed to quash any he found.

Switzerland - At the same time, OSS officer Allen Dulles was contacted by a group of Japanese living in Switzerland including the Japanese attaché to Switzerland, a businessman, a reporter, and eventually a couple of bankers. They tried to create a chance for negotiations via friends in the Naval office, but the Japanese Naval office and the Foreign office both basically drug their feet. In the end they decided they didn't have enough info on Dulles to consider him a viable negotiating partner, and they didn't trust the Japanese men in Switzerland to negotiate on their behalf. So they dithered for months, and the Americans more or less gave up on those negotiations. But it should be noted that Dulles was authorized by the State department to negotiate, and the US officially left the channel open, the Japanese just never reciprocated.

In both the Swedish and Swiss cases it wasn't the official government which was offering to negotiate, but private individuals or low level officials. And despite having high level contacts within the government, they could never get the Japanese government to give them authority to negotiate, or instructions on what to negotiate.

There was an attempt to start some sort of official meetings using the Soviets as intermediaries. But even that was a point of significant disagreement among the cabinet. Officially they were still releasing documents like the June 6th memorandum that stated their intention to "prosecute the war to the bitter end." And the meetings with Yakov Malik were more focused on trying to get the Soviets back into a neutrality pact than to start negotiations with the Americans. Even as late as the June 24th meetings, Japan hadn't given Malik any concrete proposals for how to conduct negotiations let alone any actual peace proposals.

On June 13th PM Suzuki used the word "peace" in a speech to the Diet, and was roundly booed by the body. There were even suggestions that he get a vote of no confidence for having simply used the word peace in a speech. The Japanese finally selected an official negotiator on July 12th, Prince Fumimaro Konoe. But they couldn't provide the Soviets with even a vague description of what his mission was going to be. So he never even left for Moscow. Negotiations via the Soviets were incredibly slow. Negotiations via Sweden and Switzerland, never even got started. And all official communications explicitly stated Japan intended to fight to the end.

That's how things stood on August 6th. All unofficial peace feelers had been quashed by Tokyo. The official negotiator hadn't talked to a single person. No official offer had been made. And officially the government had rejected all other attempts at communication, let alone negotiation.

Unofficially the US had broken Japanese diplomatic codes and knew that there was a peace faction in the Japanese cabinet. But that faction was clearly out of favor and the Allies had no one to negotiate with. If the Japanese were trying to negotiate or surrender they weren't trying very hard. So no one on the Allied side was taking it very seriously.