I feel Shaquiri, while never going to be a top player, would make a decent option for a top-6 club to have on the bench and playing occasionally. At Liverpool if, for example during the CL final, it were the option of bringing on Lallana or Shaquiri I'd pick Shaquiri.
Perhaps he doesn't want that and prefers to be playing regularly, and I suppose that should be commended these days.
At Newcastle or Everton level I think he'd get regular game time, but not much higher. Could be a relative bargain or loan for someone, as Stoke will want his wages off the books. Perhaps Leicester will be interested if Mahrez leaves as expected.