Nuno Espirito Santo and David Moyes have emerged as two of the leading candidates to replace Carlo Ancelotti as Everton manager.
However, he has quickly turned his mind to who might replace the Italian.
At a meeting of senior figures at the Goodison Park club, it is understood the names of former Wolves manager Nuno and West Ham boss Moyes were prominent.
Moshiri was impressed by the job Nuno did during his four seasons at Wolves, while Moyes was close to being re-appointed as Everton boss when Ancelotti became available in December 2019.
It is understood Moyes has agreed a three-year contract to remain at West Ham, but that it is yet to be signed.