The 20-year-old spent the 2021/22 campaign on loan in the Premier League with Norwich City.
Whilst the Scotland international made 24 top-flight appearances for the Norfolk club, he came under fire for a number of his performances.
Gilmour was singled out by some travelling Canaries fans for his display during Norwich’s 3-0 pummeling at the hands of Crystal Palace at Selhurst Park in late December, with manager Dean Smith later coming out and defending the youngster.
90min have reported that another loan move for Gilmour is on the cards, with Fulham, Bournemouth, and Rangers all named as possible destinations for the 2022/23 season.
However, with Frank Lampard now in full flow with the Toffees, Brown believes that a move to Everton could be perfect for the young Scotsman.
Speaking with GiveMeSport, the Daily Star journalist claimed: “I think if Chelsea were to allow him on loan again, I suspect they would quite like him to go and play for Lampard because they know Lampard will look after him.
“And I think even if he doesn’t play every game, he would be an asset, so that seems like a move that would suit all parties to me.”
Former Rangers striker Kenny Miller hailed the 20-year-old during their time together at the Glasgow club, claiming that Gilmour is a “special talent”.
Whilst in charge at Chelsea, Lampard was also full of praise for the youngster. Dubbing him an “outstanding” player, the current Toffees manager handed the Scotland gem 17 senior appearances for the west London outfit, two of which came in the Champions League.
Therefore, despite an underwhelming spell at Norwich, a loan move to Everton could revitalise Gilmour’s career in the Premier League, particularly with a trusted, familiar face in Lampard to guide him along.
