Everton boss Carlo Ancelotti is waiting to see if Theo Walcott will be fit to face Arsenal this weekend.
But the Italian did confirm that Bernard had recovered from a minor knock.
"Bernard is training normally," said Ancelotti.
"Walcott continues to have problems with his knee, he's not trained.
"We hope in the next few days he can start to train and be available for the game against Arsenal.
"But until now he did not train.
"The others [who were fit for Palace] are all okay, no problem."