Davey has been in charge since November 2006 and has led The Reds away from relegation three seasons in a row, but 2008-2009 has been a disappointing campaign and Cryne will sit down with Davey to discuss future plans.
Cryne told BBC Radio Sheffield:
"He has to make a persuasive case to me why he should stay in charge.
"He then needs to take that case out and explain it to the wider fan-base."
"I want to hear more about what his plans are for Barnsley Football Club.
"That will be a key issue in our discussions, and whether he's got that ability to build a rapport with our fans."