Allan Johnston will hold further talks with Kilmarnock chairman Michael Johnston in the next 48 hours about the managerial vacancy at Rugby Park.
The Queen of the South boss met Killie chairman Michael Johnston on Thursday.
Johnston, who is the number one candidate for the post, wants time to consider his options and has not ruled out remaining with the Dumfries club, BBC Scotland has learned.
The position became vacant after the sacking of Kenny Shiels.
"I'm still hoping to have someone in place for Monday when the players return for testing," said the chairman.
"Our pre-season training schedule starts the week after and it's important we have someone in place before that."
Former Kilmarnock player Johnston, 39, led the Doonhamers to Second Division title victory and Scottish Challenge Cup success last season.
However, Sheffield United coach David Unsworth has ruled himself out of the Kilmarnock vacancy, BBC Scotland has learned.
The former Everton defender met Killie chairman Michael Johnston on Sunday but has decided to take himself out of contention for the role.
"We have a number of strong candidates under consideration, all of them possessing different attributes," said the Rugby Park chairman earlier this week.
"It is always good to see the level of interest that we have seen in the managerial position at Kilmarnock since it became vacant.
"We have received 40 applications. Some of them have come from older candidates who have worked at some very big clubs across Europe but are looking for a change of scene.
"Others are UK-based and younger. They are just starting out but have good coaching credentials.
"Allan would fall into that latter category.
"Allan's only been in management a year but has proved himself by winning the Second Division championship and also beating Rangers with Queen of the South at Ibrox .
"He's a former Kilmarnock player, still lives locally and knows the Scottish scene. He knows how to work with a tight budget and young players and he's ambitious.
"We are looking for a long-term relationship but I know that ambitious managers will want to try it out down south. We have frequently seen managers move from the SPL to England."