There are two issues surrounding a new Max Payne game: after everything he's been through, where is there for the character to go? Has the linear style of gameplay from the previous games now had its day?
Well, Rockstar is a master of re-invention. Should a new Max Payne ever see the light of day, expect it to be a massive move away from games of old. With the open-world style of gaming now more popular than its ever been, don't be surprised to see Max move into more of a GTA-type universe (his last incarnation did have a bit of Michael De Santa about him). As for what new personal horror and tale of redemption our hero could face - maybe being forced into some kind of suicide mission is something to consider? I'm sure if the game is does get made, Rockstar will think up something suitably grim and dark - but one that always concludes on a positive message, naturally.
Out of all the franchises Rockstar owns, Max Payne is likely to be quite low down on the list of ones to reintroduce. A reinvention of the series would be something to look forward to, especially for fans of the previous games, but seeing it at next year's E3 would be a surprise, albeit a nice one.