23-old Moore who is out of contract has already been offered a final deal by the Railwaymen.
Moore netted the second goal in the 2-0 win over Cheltenham Town at Wembley last month taking his tally to 10 for the 2011-2012 season.
Any move for Moore over the border would result in the club receiving nothing in compensation where as if an English team wanted to sign the Stoke born forward would have to pay compensation.
Hibernian manager Pat Fenlon is keen to bring Moore to Easter Road but faces competition from Craig Brown's Aberdeen.
Crewe Alexandra boss Steve Davis is keen to stop his player heading to Scotland, and had a dig at the SPL, the Crewe boss said:
“Why he would want to move to Scotland I’ll never know.
“We’ve had talks with Byron’s agent and we feel we’ve made him a very good offer. It’s our final offer and now it’s down to Byron.
“He’s just had his best season with us since I’ve been here and if he stays in the group he will continue to improve his game.
“Maybe if he goes he would be able to earn a little bit more money but if he can carry on performing and scoring goals in League One there will be other clubs much higher up the pyramid who will be looking at him. He needs to decide.
“If he moves to another club in this country we will get compensation but we won’t if he goes to Scotland.
“We are here to offer advice and I think he should stay with us for 12 months more.”