His initial month's loan is due to run out immediately after Crewe's League One match at Preston a week on Saturday, but Davis wants to sort out the striker's future before then.
He said: "It depends on Lauri. Whatever we want to do, it will depend on whether he wants to stay or go back.
"But I do know he is thoroughly enjoying his stay here and enjoying the football we play.
"He is getting his rewards because of that and is working very hard for the team. It is brilliant when you get players like that coming along.
"Normally you have to get them fit, do some work with them and integrate them, but he is the sort of lad who does exactly what he is told to do.
"He has found it very easy to make the transition and has been a breath of fresh air for us."