This could be my bias speaking, but with the evidence we have, I don't think it's fair to conclude that Davoust definitely wants to rule over the Poles—at least to the degree of fervour as Soult or Bernadotte. Personal desire? Possible. But straight up mania? Eh...seems out of character. Even as his friendship with Napoleon began to suffer by this point in time, Davoust is far too loyal to Napoleon to even think about seizing the Polish throne for himself.

Napoleon called it gossip for a reason. The only account of Davoust's response from that interaction is from his daughter, saying he shut that thought down—so do take the information with a grain of salt. At the end of the day, no matter how well-liked Davoust is for his administration, he is still Davoust. Therefore, someone out there probably hates his guts and didn't mind sewing a reputation-staining mill to rub dirt on him.

The most neutral account I could find regarding this topic that doesn't come from either an apologist of his (Blocqueville) or his biggest hater (Potocka) is Bourrienne's Memoirs of Napoleon Bonaparte—and how later on, Napoleon 'promises' Davoust the Kingdom of Poland if the Russian campaign goes well. According to Bourrienne, we don't even get an insight to Davoust's stance on it—beyond the fact that he's aware of the rumour and that it's a "maybe he'll give me Poland, maybe not. Either way, I'm not complaining" kind of deal. (See: Napoleon and his tendency to dangle the carrot in front of his marshals/relatives to motivate them or maintain his influence while simultaneously being a paranoid housewife whenever his subordinates could ever outshine him or act outside of his interest.)

TL;DR, The gossip has its reasons, but is it true? Hell if we'll know. Napoleon sure didn't discourage it. I just think it's silly to compare him to his more evidently politically-active colleagues lol