The Dutchman is healthy and ready to play, but Allardyce has seemingly made his mind up that Klaassen isn't good enough to play in his side.
Klaassen, who joined from Ajax in the summer, has not played for the Toffees since December. And it seems his cold streak is set to continue under Big Sam.
"At the moment Davy Klaassen comes in and trains as best as he possibly can and does all what he can on a regular basis," Allardyce said.
"He's not a sulker, he tries his hardest everytime he comes into training.
"But at the moment we see what we see, and we see the qualities of the players and haven't quite seen that in Davy to encourage us to put him in.
"He's got big competition and that big competition is something you have to accept and try and improve so if you do get the chance then you take that opportunity.
"Maybe somewhere down the line we will give him an opportunity."