The youngster was on loan at RB Leipzig last season and was linked with another move away from Everton.
But, despite Richardson’s arrival and talk of more signings today, he will stay put.
Myers said: “One significant piece of information is about Ademola Lookman. There’s been lots of interest in him. RB Leipzig have tried everything to get him out of Everton but I can tell you 100 per cent he’s staying at Everton.
“I’m also told he’s going to be a very big part of this season. So good news for Evertonians, Ademola Lookman will be staying at Everton.”
Lookman, 21, is wanted by Marco Silva, who this week said: “He is our player and he stays.”
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Everton are trying to get deals for Yerry Mina and Andre Gomes over the line today.
Both players are believed to be having medicals to sign before the 5pm deadline.
While Bernard is also close to completing his move.
“They are close to bringing Bernard in, the former Shakhtar Donetsk winger,” Myers told Sky Sports News.
“We saw him yesterday arrive at Manchester Airport to complete the free transfer.
“He’s very close, the medical was done yesterday and I expect an announcement to be confirmed later this morning.
“The other big news at Everton is about Yerry Mina. My understanding, I’ve spoken to somebody in Spain this morning, is that one is very, very close to being done.
“It’s been a long, long saga has the Yerry Mina saga. There’s been plenty of names, clubs who have been after him.
“It looks as if Everton have won the race to win the Colombian centre-half.
“Andre Gomes as well of Barcelona has been mentioned, I’m not sure that’s one that’s quite as near.
“But certainly it’s going to be a very, very busy day here at Finch Farm.”