Which audience?
The audience who's only/mostly interested in reissues and/or retreads? I'd say that that audience is pretty much already connected. It's a small one, but hell, what do you expect?
The audience who wants to hear challenging new music that doesn't replicate the old? There's an audience for that, even if it is smallish and fragmented, but everytime you call most of that music "jazz", cries of righteous indignation are heard across the Land Of The Guardians.
The audience who wants to hear entertaining instrumental music that's not too unfamiliar/complicated/confrontational? That type of jazz is already pretty well connected with its audience, be it Smooth or Jam or whatever.
The audience who wants jazz to serve in the role of Official American Cultural Triumph? Again, connected. Lincoln Center's doing good business.
Jazz as we've known and loved it is pretty much dead as a vibrant musical form of today. Evolution works. But jazz as a mindset/spiritual vibe will never die. Hell, it existed before jazz as a musical form ever did, and it lives on today.
It's the jazz audience that needs to reconnect with today, not jazz music with its audience. I could someday maybe even be persuaded under the right circumstances to say that it's the audience that's killing the music, not the other way around.
Do we want our children to know and appreciate the great musical and spiritual legacy of jazz? Damn straight we do. But what do we want them to do with that knowledge and appreciation? Regurgitate it in perpetuity, or do something of their own with it? We say that we want the latter, but then too often recoil in horror when the results aren't comfortably similar to what's gone before.
Bodies dying is natural and healthy. Spirits dying isn't.