The Merseyside club have been heavily linked with the former, who is thought to be surplus to requirements at his current side Tottenham.
What is the latest transfer news involving Everton?
According to Sky Sports, Everton are interested in signing Winks and have been given the green light by Lampard to make a move for the player.
Winks’ career at Tottenham looks all but over, with the same outlet claiming that the north London club have told him to find a new team this summer.
The 26-year-old made just nine league starts last season, and you would expect that number to drop further next term following the arrival of Yves Bissouma.
Regarding how much he could cost, the Daily Mail reported towards the end of May that Spurs were looking for up to £25m for the midfielder.
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What has Brown said about Everton’s transfer plans?
Brown has told GIVEMESPORT that Lampard is definitely keen on bringing in a player of Winks and Gilmour’s profile.
Speaking to GMS, the Daily Star journalist said: “Everton still don’t have a kind of ball-playing, deep-lying midfielder. It’s one of the reasons why they brought in [Donny] Van de Beek in the transfer window, and I think he’s still looking for that.
“Harry Winks is someone who can play that role. He obviously likes Billy Gilmour as well. Whether he’s ready to take on that kind of responsibility at a big club like Everton week to week is still to be decided, but I think Lampard is definitely looking for that profile of player.”
Who should Everton sign, Winks or Gilmour?
There is no denying Gilmour’s talent and potential, with Liverpool legend Graeme Souness backing him to become a “fabulous little player” in the future.
However, he did have his struggles at Norwich City last season and was dropped by Daniel Farke before his sacking, while the Chelsea youngster is obviously not as experienced as Winks.
Given where Everton were last season, fighting for survival, bringing in a more seasoned midfielder like the England international may be the wiser move.
Being a big fan of Gilmour, though, Lampard would still probably be happy if his former Chelsea player arrived at Goodison Park instead of Winks.