And his chances of doing so have been boosted by the news their hosts could be without two important defenders.
England international Branthwaite is a doubt for the match after suffering a dead leg in last weekend’s 2-2 draw with Hull City, while the full-back Mykolenko is sidelined with a knock suffered on international duty.
"Jarrad had a problem. He got it really early [against Hull],” Moyes explained on Friday. “We've been looking at that in the week.
“Myko's doing much better. Myko's got a chance for the game.”
Jarrad Branthwaite picked up a knock against Hull last time out
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He continued, saying the summer signing Norgaard is still not ready to start.
The former Arsenal midfielder has yet to appear for Everton after he arrived at Finch Farm carrying an injury. He trained during the international break and Moyes feels he is ready to feature, but not yet fit enough to feature from the off.
"Christian's still got a bit to go,” Moyes added. “A wee bit to go. I think we could use him at certain times if required, but I don't know if he's ready to start the game yet."
Chelsea may come up against one of their own on Saturday afternoon, with Moyes suggesting Tyrique George could be in line to feature. The young winger came through the Blues’ academy and spent the second half of last season on loan with the Toffees before making the move permanent in the summer.
He has been in and out of the side this season, though, as he competes with Jack Grealish for minutes, but Moyes has made clear he welcomes the competition.
"I think Tyrique's knocking at the door. I think he started a wee bit slow and then picked up. So, there's huge competition in that position. Jack's aware that Tyrique is there.
"He's done well for us, Tyrique. We've enjoyed it, we bring him on and we think he can do a job for us on both sides."