I heard that Tenseigan can be awakened by those having both Otsutsuki and Hyuga blood lines. Boruto has Otsutsuki blood from Naruto (A descendant of Hagaromo Otsutsuki) and Hyuga blood from his mother. Can he awaken the Tenseigan?
At the moment it is possible, due to the Uzamaki clan being very vaguely related to Hagaromo (It has been a lot time for dilution of the bloodline). So he could end up with the Tensaigan, but it would be much more likely for the Tensaigan to appear in the theoretical children of Boruto and Sarada, due to Sasuke's bloodline having the optical powers of Hagaromo.
So to sum it up, Boruto could end up with the Tensaigan some time in the foreseeable future.
I believe that Boruto's eye is a completely new ability that we have not seen yet.
First of all, Boruto's eye is not a byakugan. This is pretty obvious because it looks COMPLETELY different from byakugans(no veins, only in one eye, different color). It may have similar abilities as the byakugan, but it is not the byakugan.
Secondly, his eyes are not the tenseigan either because it looks completely different as well. Sure, both may have blue, but the blacked out portion of Boruto's eye indicates a clear separation from the tenseigan. The tenseigan also doesn't have the curse mark like thing around the eye that the older version of Boruto appears to have (see image below). The tenseigan can only be acquired by combining the chakra of the Hyuga clan and the Otsutsuki clan. Boruto has Hyuga clan chakra but not Otsutsuki clan. Further evidence of this is when Boruto speaks with the ghost of Momoshiki Ōtsutsuki after his fight with him. Momoshiki points out Boruto's Hyuga heritage/chakra but makes no note of any dormant Otsutsuki chakra, which he definitely would have if Boruto did have any dormant Otsutsuki chakra. Also, it is stated nowhere that the tenseigan is able to see the "evil chakra" that Boruto's eye can see.
What Boruto's eye can be is a product of combining the chakra of Asura with the chakra of the Hyuga clan. This would yield a completely new kekkei genkai.
As I said in comment also nothing is impossible so anything can happen. But according to current information it is not possible for Boruto to awaken Tenseigan. Let me explain why I said this:
The combination of the Byakugan and the chakra of an Ōtsutsuki clan member can evolve the Byakugan into the Tenseigan.
So it pretty much explain that it can Evolve Byakugan to Tenseigan by having chakra of an Ōtsutsuki clan.
So by current definition of this, it is important to have Byakugan. Since Boruto has no Byakugan so we can say that he won't be able to have Tenseigan.
Also according to this link there is one answer which really creates a little confusion but also gives us hope of some possibility :
We know that
Rinnegan = Asura + Indra (Sharingan)
Tenseigan = Otsutsuki + Hyuga (Byakugan)
Given that they're the children of Naruto and Hinata, Boruto and Himawari's heritage would thus be:
Asura + Hyuga (Byakugan) = ????????
So, it's entirely possible that a unique mixture of Hagaromo's and Hamura's chakras will result in these two, awakening a new dojutsu altogether. This could also explain why both of them lack the Byakugan, as well as their teal-colored eyes.
There is very good reason Boruto could awaken it. However, it requires him to awaken or obtain Byakugan as well as have all of the Bijuu chakra from his dad implanted within him somehow. If those conditions were fulfilled, which they could be easily, the Tenseigan should develop from his Byakugan. The nine Bijuu chakra would fulfill having Otsutsuki chakra since Naruto's chakra is Six Paths' chakra.