I wrote about the status of Danzig during the interwar period in my undergrad. Its status was obviously a contentious issue between Poland and Germany throughout the entire time, and took on an international context as well, being controlled by the League of Nations.

However I don't belief Chamberlain ever supported a change in its status, either for Germany or Poland, but I'll admit his views, and that of the British government in the 1930s, was not the focus of my research. I am sceptical of it though, based on the fact that Britain had declared their support for Poland, and as the Poles wanted Danzig for themselves, it seems unlikely the UK would support it going to Germany. This also would have effectively cut off Polish access to the Baltic Sea via the so-called "Polish Corridor," which had been a major issue of debate during the Paris Peace Conference in 1919. Conversely to give the city to Poland would have almost certainly meant war, as the Nazis had become firmly entrenched in the Free City government (taking power just after Hitler became Chancellor, in April 1933).

Danzig was just too important to the status quo of interwar Europe to belong to any one power, and giving it to any state would have upset a delicate peace that existed at the time between Poland and Germany, and with it France, the UK and almost certainly the USSR (as well as Czechoslovakia, Lithuania, and others). So it's unlikely Chamberlain wanted to do something like this, but ultimately that is just an educated guess. If someone has a clearer idea of Chamberlain's views on Danzig, I'd defer to them on the matter.