There will be further talks this week with both Frank and Vitor, with Frank due to discuss the vacant manager's job at Goodison Park.
A number of candidates are still being considered for the job of replacing Rafael Benitez.
The former Porto manager is in talks with the owner of the company, while the former coach of the club is close to a decision.
No contact has been made with Derby County with regards to Wayne Rooney, who has also been linked with a possible return to his club.
He was a candidate for the manager's job twice before, but missed out on the job.
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The Belgium FA did not want their head coach to leave before the World Cup so that's why the club won't be able to get him.
Duncan Ferguson is taking training in the meantime, as a decision is not thought to be imminent.
It is thought that a decision will be made sooner rather than later, with important games againstNewcastle andLeeds on the horizon.
Ben Grounds had an analysis.
Two years ago, when Silva was dismissed, one man who was heavily linked to becoming his successor was Vitor Pereira. The 53-year-old was the leading candidate before he removed himself from the application process.
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While managing in the Chinese Super League, Pereira exclusively told Sky Sports: "It's always an honor and I am grateful to be considered on a list by a club that I have so much respect for." I am still the coach of SIPG, a club that is close to my heart in a country that is growing immensely in football.
I am not in a position to make any other commitments. I need time to think and plan my future, I can't make a decision now.
It is a league I love and I would love to consider an opportunity in the future.
There are reports in Portugal that he is on his way to Merseyside for advanced talks with the club, which he was considered by in the past.
The Turkish giants are in fifth position in the table and 14 points off the leaders, thanks to an unsuccessful stint by Pereira. Why is he in the frame again if he wasn't appointed in the first place?
His admirers will point to the fact that he has managed a number of top European clubs, including Porto, where he won back-to-back Portuguese top-flight titles.
1860 Munich was demoted to the German third-tier in his six months as manager.
In his first season, he only won six of his 20 games, leading to recriminations over who was responsible.
An 1860 Munich club statement read at the time that nobody around the club wanted us to go to the third division. There are only winners in such a situation.
There were no winners from the appointment of Benitez.
The super agent was spotted at Goodison Park on Saturday, and he was spotted in the director's box.
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It's not clear whether Pereira is the right person to take over at a time when the club are in the midst of an identity crisis and at the wrong end of the table.
His previous experience in a battle for survival suggests he isn't the one currently needed.
After the Belgian FA blocked an approach for a return, a search which started with Frank Lampard, Wayne Rooney, Jose Mourinho, and Martinez being sounded out for a return, has now come back to the perennially-linked Pereira being.
He will want to prove his best days in the dug-out are still to come. The international break in January gave the team some time to think about their next move.
The dilemma for Moshiri is that the manager he needs to get them out of trouble is probably not the one he needs to turn around the club's fortunes.
There is no director of football, head of recruitment or scouting at the club. It means that Moshiri will have final say.
He doesn't have to make snap decisions, but he has to make sure he doesn't get it wrong again.
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