Earlier in the day, Advocaat quit just three months into his job as assistant to Netherlands coach Danny Blind.
The Turkish sports newspaper Fanatik said Advocaat had confirmed his appointment, saying he thought he would not return to club management but that Fenerbahce had made him "an unbelievable offer".
Fenerbahce host Grashoppers Zurich in the first leg of playoffs for the Europa League on Thursday.
The Istanbul team said in a statement that they cancelled Pereira's contract after he had violated terms of the deal. The issue will now be taken to soccer's ruling body FIFA and the Court of Arbitration for Sport.
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A brief Dutch FA statement said Advocaat had "indicated he is going to work somewhere else".
"I am shocked and disappointed," said Blind who wanted the 68-year-old to help him as the team sought to overcome the disappointment of missing out on Euro 2016 by qualifying for the 2018 World Cup.
"When I approached Dick last year to be assistant he gave me the impression he wanted to do it long term. But...we have to carry on, from now on what is important is our upcoming matches against Greece and Sweden."
As head coach, Advocaat took Netherlands to the World Cup in 1994 and the European Championship 10 years later.
His last job as a club coach was with English Premier League Sunderland where he resigned last October.
(Reporting by Mark Gleeson and Ece Toksabay in Ankara, editing by Tony Jimenez)
