Pep Guardiola insists Mikel Arteta will not be leaving Manchester City before the end of the season.
The pressure on Unai Emery intensified after the Gunners were held to a 2-2 draw by Southampton on Saturday.
Toffees boss Marco Silva is also in a precarious position after his side suffered a 2-0 home defeat by Norwich.
Arteta played for both clubs before hanging up his boots in 2016, making him a potential candidate for the top job at the Emirates Stadium and Goodison Park.
But although Guardiola thinks his assistant will become a manager in his own right one day, the City boss says he is not going anywhere until next summer at the earliest.
"Unai Emery is the manager of Arsenal," said Guardiola. "[But] of course [Arteta] will be a manager sooner or later. We are going to finish the season but in the future I don't know what is going to happen.
"I would like him to stay with us. Manchester City has a person of incredible value to work here in the future. But professional desires are professional desires. Everyone is more than satisfied to have him here.
"He was an incredible player. The holding midfielder has a vision of what happens on the pitch. When you are a striker you think of the goals and 'keepers to save it.
"But I think that the holding midfielder is an incredible lesson during your period as a football player. You don't need to go to school.
"More than that he is an incredible human being and works a lot. I said after a few months together he would be a manager. He is already a manager - he behaves like a manager."
City will qualify for the knockout stage of the Champions League if they avoid defeat against Shakhtar Donetsk on Tuesday.
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