Italian speedster Gnonto is looking to leave Elland Road and the Toffees believe they can land the 19-year-old for a bargain fee.
Gnonto cost Leeds just £4m from Swiss side FC Zurich last summer, but showed his qualities with four Premier League goals and a string of eye-catching performances.
Leeds are under pressure to sell after dropping into the Championship, although Gnonto is not believed to be among a number of their players with relegation release clauses in their contract.
The youngster also has interest from Serie A although his preference is to stay in the Premier League.
The talkSPORT notebook revealed earlier this year that Chelsea have been keeping tabs on Gnonto, the youngest player to score for the Italian national team.
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Gallagher set for fresh chance
Conor Gallagher is set to reap the benefits of Chelsea's summer exodus by being handed the chance to prove to new manager Mauricio Pochettino he has a future at the club.
Gallagher was among a host of homegrown players including the departed Mason Mount and Ruben Loftus-Cheek that Chelsea had earmarked to sell for decent profit.
But despite interest from a host of Premier League clubs including Brighton and West Ham, sources close to Gallagher now believe he could stay at Stamford Bridge and compete for a starting birth.
Chelsea have already offloaded Mount, Loftus-Cheek, Kai Havertz, N'Golo Kante and Mateo Kovacic, leaving them short-handed in midfield.
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As well as Gallagher, Pochettino will also cast a keen eye on Brazilian wonder-kid Andrey Santos, 19, during pre-season.
Chelsea to face off with £100m target
Chelsea target Moises Caicedo could feature in their pre-season tour of the USA - by playing AGAINST the Blues.
Caicedo is new Chelsea manager Pochettino's top summer target, but Brighton are holding out for a Declan Rice-sized £100m fee for the Ecuadorian.
With no imminent sign of an agreement between the two clubs, Brighton are planning for Caicedo to be part of their travelling party when they themselves head for America.
Brighton and Chelsea are scheduled to meet each other in Philadelphia on July 22.
Owner Tony Bloom showed he is no pushover when it comes to transfer negotiations by rejecting two big-money offers from Arsenal for Caicedo in January.
The midfielder signed a new contract soon after the transfer window closes, which, crucially, did not include a release clause allowing him to leave for a set fee.
Luton target Premier League experience
Ashley Young has emerged as a surprise target for Premier League newcomers Luton.
The Hatters have explored the possibility of signing former England defender Young, who turns 38 on Sunday in a bid to add top-flight experience to their squad.
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Given he started his career at the Hatters' arch-rivals Watford, Young could be forgiven if he was reluctant to make the switch to Kenilworth Road.
Young is a free agent after leaving Aston Villa.