Everton allowed Jack Harrison to leave the club at the end of the season, where he returned to Leeds United.
David Moyes is pushing for a new winger, and he has been after attacking additions since he returned in January.
The Toffees have added Thierno Barry already this summer, but the Blues are going to need some added quality around him.
Everton are running out of time if they want any further new signings on the plane departing for the United States next week.
The Friedkins have offered Everton a £100m budget, but the number of additions needed will require the Blues to make the most of loans and free signings.
It has even been suggested that Everton could offer Harrison a return to the club following his two-year loan.

Whether Everton will offer Jack Harrison a return this summer
Everton would bring Harrison back as a free agent, but that would require Leeds United to terminate his deal.
Given he still has a number of years left in Yorkshire, it is asking a lot for Leeds to reach an agreement with Harrison over his deal.
Taking to social media, Alan Myers has shared what Everton were suggesting at the end of the season about a return for the winger.
‘I don’t know, heard suggestions just after the season that he might be back, but nothing since,’ he said.
It has been suggested that Moyes would be open to Harrison returning to the club over the coming weeks.
Harrison would provide the Toffees with a familiar face who could seamlessly return to the fold.
However, big questions need to be asked as to whether the player has the quality Everton are looking for going forward.
David Moyes demanded more from Harrison at Everton
Although it’s been claimed Moyes could green light a return for Harrison, he was not always impressed by the winger’s output.
Moyes demanded more goals from Harrison and Jesper Lindstrom last season.
However, Harrison was only able to score once in the entire Premier League campaign, which is severely underwhelming.
The Friedkins want to make a statement signing this summer, which will mean lower-quality players will be required to build up the numbers.
But Everton have already been there and done it with Harrison.
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