The 21-year old Finland youth international joined the Alex earlier this month and his short-term spell is set to expire early in December but Davis is hoping he can come to an agreement to keep him at Gresty Road.
"It is something we have talked about. We have just over a week to decide and it is something we will do sooner rather than later," Davis told The Sentinel.
"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. He has found it very easy to make the transition and has been a breath of fresh air for us."
Dalla Valle has made a huge impact at Crewe, scoring four goals in five starts, with the three matches he has tallied in bringing home wins for the club.