Kone has been brought in by boss Roberto Martinez from his old club Wigan while Deulofeu is an exciting arrival on a season-long deal from Barcelona.
Both should start as the Martinez era begins but who will partner Kone up front is less clear – with both Victor Anichebe and Nikica Jelavic hoping to get the nod.
Elsewhere, another summer signing Antolin Alcaraz has a hamstring injury so will miss out while new goalkeeper Joel Robles is likely – for now at least – to be used as substitute with Tim Howard starting the campaign as number one.
Marouane Fellaini has a knock and is not available, while Darron Gibson and Tony Hibbert are major doubts for the Carrow Road trip.
Falkirk attacker Louis Longridge is more than familiar with the underdog tag the Bairns will take to Ibrox on Sunday.