Cap Friendly confirms that existence of the clause in his contract.
Larry Brooks writes that the Rangers are "unlikely" to allow that clause to come into play and would likely carry him on the roster. (NY Post)
Pavel Buchnevich is believed to have a similar clause in his contract.
Adam Rotter: The Rangers signed Bereglazov in April and then went on to sign Neal Pionk, re-sign Brendan Smith, acquire Anthony DeAngelo and sign Kevin Shattenkirk. At the time the Rangers signed Bereglazov it was clear he had a much better shot at making the roster than he does now. If the Rangers move on from Nick Holden his chances increase but he will still be battling DeAngelo and Pionk for that spot.
It's hard to compare the situation to the one with Buchnevich since Buchnevich was the Rangers top prospect, had spent the summer in the NY area adjusting and there were spots available up front. This is something that will play out in training camp but in the event that he doesn't make the team and decides to go back to Europe, is his still property of the Rangers? Could he return to the Rangers in the event of injury. There seem to be a lot of different potential factors in play in this situation.