Allardyce has met with Dyer to discuss his future at the Tyneside club and told Sky Sports the situation.
"At the moment, there's a problem from a family point of view and we have to try to see whether we can resolve that, and if we cannot, then that may well result in Kieron looking to leave the club for that reason and that reason alone.
"That's the discussion we have had. It's obviously disappointing for me, but it is one I understand.
"If somebody has got a problem they cannot resolve, then ultimately in the long run, it is better for the club and better for him if you can resolve that problem.
"If that's away from here, then so be it."