I'm trying to read the tea leaves here and see what this potential inquiry means for all the other moving pieces - especially since you know the Jazz have been talking to Hayward and Hill and have a pretty good idea of where things stand.
Scenario 1a) The Jazz know that Hayward and Hill will resign if we get another major piece - Love, George, etc. In order to get one of those players, they're going to have to trade away some combination of picks, Favors, Hood, and Exum. Acquiring Beverly replaces either Exum or Hood on a cheap contract that will allow the Jazz to fit in the salaries of Hayward, Hill, and another big piece.
Scenario 1b) The Jazz know that Hayward will resign if we get another major piece like Love or George, but it can't be done while also meeting Hill's salary demands. They bring in Beverly and have Beverly and Exum fight over the PG minutes, trade a package of Hood + picks for someone like George, or Favors + picks for Love.
Scenario 2) The Jazz know that Hill is leaving and are doing anything possible to convince Hayward to stay, and Beverly is one of the few options available where they think they can stem the bleeding.
Scenario 3) The Jazz know that both Hayward and Hill are leaving but want to provide Gobert with a competent floor general in order to keep him happy while they figure out how to restructure around him.
Interestingly, I think scenario 3 is the LEAST likely here because knowledge that both Hayward and Hill are leaving means that it's going to be a long road back to competitiveness and it's important to try to strike gold in the draft rather than give them up for someone who doesn't truly move the needle on the team.
I think this is a sign that they're working on something involving Hood, Exum or both, and they're either convinced Hayward is going to stay or is close to staying, as long as they can improve the team with another borderline or actual All Star. Beverly is not that person - he's a facilitator to make the math work.
Any other scenarios I might be missing?