Martinez had asked for 24 hours to consider his next move on Wednesday, but after meeting Whelan again on Thursday it is the chairman who has now gone away to consider whether he can match his manager's ambitions.
And he stressed the discussions were solely focused on taking Wigan forward and had not touched on Martinez's personal situation.
"We have had a good, constructive talk - nothing about wages it is all about the club and can we move it forward in terms of the training facilities and youth development," Whelan told Press Association Sport.
"It is all tied up in that. He wants to do certain things and I'm hoping I can assist in that but I want a day or two to look at it.
"I don't want to say yes until I've had time to think about it. It will be Monday before I can promise anything."