It's been said that Legend of Conan will be his Unforgiven; his last ride(have to assume). So, once that is done, a reboot closer to Howard's roots can finally occur. Speaking of Robert E. Howard, Kull is another of his properties that could be apt for a reboot. If not cinema, maybe Netflix or HBO.
Depends on studio outlook, not Arnold's. The tried and proven over the untested. Imagine you're a studio exec and try not to think like a Conan fan. You're making a Conan film, your job is on the line and you can be fired if it doesn't succeed. Do you use the tried and proven formula from the past that people are familiar with and just recast a current young action hero like Tom Hardy? Or do you take a risk, not go the tried and proven, and bring audiences a version of Conan that has yet to be tested if your job is on the line?
Didn't mean to say, if you took it that way, it relied around Arnold. It relies around suit hesitation to taking risks. We all know the keep the old hero, just recast younger, like the back of our hand. The Arnold complication is this - whereas his Conan version used to be old, 30 years or something from the past - meaning it makes it untested among audiences that have come since then, with a new version if that does well - it becomes the version audiences are familiar with again and if that does well, it becomes a modern day tried and proven approach. With it being old there's a level of uncertainty attached to it (but the most certain form to suits) with it being new and working again - it reignites that old approach as being seen as "safe because that made bank today."
The best recent fan example of seeing that in play is 'Superman Returns.' They could have given us all an awesome Superman film that's original, a new and daring take that relies on the comics that so many love. Their thoughts went to "how can we make this more like Burton's Batman?" and when that didn't work out "can we remake Donner?" They had a lot of new places they could go because of the comics, instead they chose to go the way that had worked in the past - it took seeing that mistake with Superman to bring about a film that wasn't connected to the past. For Singer that approach came from love for the original, for the guys paying for it - that approach came from seeing the dollar signs from the past coming back.
(this is why a lot of people, especially creatives, hate suit notions (or rather hate financial notions and stats) - although, from having worked alongside them - they are more than understandable as well because their job is on the line with it. So, they are forced to look at the financial and numbers side of it not the creative one. And comically yes, they do go back and reshoot some titling shower scenes of their hot actresses to draw crowds in, one of which I can say they reshot because they needed something like that for a comic-con trailer to draw you guys in (Peter Jackson's hilarious commentary on the studio system in 'King Kong' is spot on a comedic caricature)).