And it would appear Everton will likewise have to plan without Fellaini at least until the start of next season.
Fellaini had been set to visit the specialist last week before his train to London was cancelled.
Speaking last week, Moyes said: "He's got a really bad ankle. I was really surprised - it was like an elephant's ankle, it was that bad.
"He has been integral part of how we have played in recent weeks and he will be a miss."
Greek defender Kyrgiakos was sent off for his part in the tackle during a typically fiery derby encounter at Anfield.
However, some observers contended that Fellaini was equally at fault, with television replays suggesting he connected with Kyrgiakos's shin.
However, after the game Moyes backed his player - and continues to do so.
"I haven't changed my views, that it was a two-footed tackle off the ground [by Kyrgiakos]," said Moyes. "He was flying towards a player, he could see that coming all the way, so it was a sending off."
The Belgian international has been enjoying the best form of his Goodison Park career since his arrival on Merseyside for a club record fee of £15m in September 2008.
Moyes even claimed that Fellaini was the best midfield player in the country based on current form following his starring role in Everton's 2-0 home defeat of Manchester City last month.
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