There are numerous theories. Most think it was destroyed in the Time War. However, it MIGHT have been left in the Silver Devestation (which is where Professor Yana was found), which means it COULD still be there.
It is worth noting that we do not in fact know that Professor Yana was found on the shores of the Silver Devastation. He said he was found there as a child but then John Smith said he had grown up in Nottingham. In the latter case, this was part of the cover story and was untrue; John Smith was a fiction and had never existed as a child. Professor Yana probably didn't exist as a child, either, and might never have been near the Silver Devastation.
We know the Master used a Chameleon Arch. When the Doctor used his Arch, he said that the TARDIS would create his cover story. That strongly suggests the Arch could not function without the TARDIS. Also, the Master had to reach the time and place where he was encountered by the Doctor, which means he would need transport -- probably a TARDIS.
the Master would be unlikely to strand himself intentionally, so there is a good chance that there is indeed a TARDIS sitting around somewhere at the end of the universe. When the Master was restored to his true identity in "Utopia", the Doctor's TARDIS was immediately to hand. Additionally, escaping in the Doctor's TARDIS had the advantage, from the Master's point of view, of stranding the Doctor. Even if there were a TARDIS somewhere around and the Doctor managed to figure out that there must be one, he still would not know where to look for it.