Hitler couldn’t make up his mind. Her didn’t want the Empire destroyed, as (in his mind) the US, Japan, and possibly the Soviet Union would benefit from this.
According to Ian Kershaw in his books, Hitler originally scheduled to make a Reichstag speech (directed at the UK) Monday, 8 July. He postponed it three times, finally giving the speech on 19 July. This (again, according to Kershaw) indicates an uncertainty about how to proceed on the issue. (He believed Churchill was still pro-war, and would not respond well to any offers. He hoped others would push Churchill out of power.)
When he finally gave the speech, it was a two and a half hour speech, mostly recounting the course of the war to this point, and the might of Germany. It was only in the last few minutes of the speech did he get to his “offer”: Churchill was a warmonger. A threat that the Empire would be destroyed. A regret for the victims of war. And a final “appeal to reason”. He offered nothing that could have formed a basis of a peace lobby in London to cling to.
The UK announced it’s rejection within the hour.
Hitler assumed that the UK still clung to hopes that the US and/or the Soviet Union would enter the war against Germany. (Hitler had no illusions about Stalin being a temporary ally. He assumed that Stalin was “flirting with Britain” to keep her in the war, and tie down Germnay, while the USSR exploited the situation to further it’s own expansionist policies.)
Eventually, according to Kershaw, he decides to attack the USSR (something he had always wanted to do anyways), and, necessarily opening a two front war (even though this was something he repeatedly warned his Generals not to do), in order to remove a pillar of hope out from under Churchills war and diplomatic strategy.
IMO: It seems to me that Hitler didn’t have an answer, a plan, or any idea of an what kind of offer to bring about some kind of Armistice in the second half of 1940. Any actual concessions militarily, or diplomatically, on the part of Germany must have seemed out of the question. Anything that made Germany seem weak, or the Furher not in control of the situation, was out of the question, as it may endanger Hitlers/Nazi power in Germany, at least in Hitlers mind.