The pair spent the 2021-22 Premier League season together at Southampton, with the latter enjoying a successful year-long loan spell from Chelsea, netting six league goals in 21 starts.
The Albanian's future remains up in the air this summer, with several top flight clubs chasing his signature either on temporary deals, or permanent transfers.
Everton are one of those sides involved in the race according to the Mirror, and the report suggests that Toffees boss Frank Lampard will look to utilise his contacts within Chelsea to complete a deal.
Walker-Peters is another being targeted by Lampard during the transfer window according to the report, who enjoyed a productive 2021-22 campaign in both full-back areas for the Saints, during which he made 32 league appearances.
The 25-year-old's form led to Gareth Southgate handing him his England debut against Switzerland back in March, before earning his second cap just three days later against the Ivory Coast as well.
However, any potential deals for the pair are on hold as things stand, with the report outlining how Everton are waiting for the all clear from the Premier League to proceed with signings this summer.
The Merseyside outfit remain under investigation regarding an official complaint from Leeds United and Burnley dating back to the end of the 2021-22 campaign, with the pair claiming a breaking of Financial Fair Play rules by Everton, following several years of significant losses.
The sale of Richarlison to Tottenham Hotspur at the beginning of the month is said to have eased any immediate concerns, but Lampard's side must first wait for the green light before proceeding with a squad rebuild ahead of the new season.