The 27-year-old has spent the last four years with the Toffees, scoring nine goals and providing 16 assists in 140 appearances across all competitions, including two goals and eight assists in 38 Premier League games last season.
However, Iwobi has been tipped to leave Goodison Park this summer as he has entered the final year of his contract, and cash-strapped Everton are believed to be open to parting ways for the right price.
According to Sky Sports News, Fulham and Everton are close to an agreement over a deal for Iwobi to move to Craven Cottage before Friday's transfer deadline.
Iwobi is said to have already agreed personal terms with the Cottagers and the Nigerian is expected to travel to London for a medical once the final details of the deal are sorted.
Fulham boss Marco Silva was in charge of Everton when they signed Iwobi from Arsenal in 2019.
Sticking with Everton and they have reportedly identified West Ham United's Maxwel Cornet as a potential replacement for Iwobi.
Toffees boss Sean Dyche is familiar with the 26-year-old having previously worked with him during his time at Burnley.
Cornet has struggled to nail down a regular starting spot at West Ham since joining the club for around £17m just 12 months ago, starting just two of his 14 Premier League appearances last season, while he has only made one substitute outing so far this campaign.
The Daily Mail reports that Everton have opened talks with the Hammers to sign Cornet, with the Toffees keen to take the winger on an initial loan deal.
Cornet impressed during his one and only season at Burnley in 2021-22, scoring nine goals in 26 Premier League appearances, while he previously netted 51 times in 252 games for Ligue 1 club Lyon between 2015 and 2021.
Should West Ham agree to let Cornet join Everton on a temporary basis, David Moyes's side could reportedly reignite their interest in Juventus wideman Filip Kostic.
The Hammers were keen to sign the 30-year-old last summer before he left Eintracht Frankfurt to join Juve for around £13m.
Predominantly operating as a left wing-back, Kostic scored three goals and registered 11 assists in 54 appearances for Juventus last season, but the Serbian is yet to play a single minute for Massimiliano Allegri's side this term.
According to the Daily Mail, the Italian giants are open to offers for Kostic amid renewed interest from West Ham and they will demand at least £13m for the versatile winger.
Meanwhile, Calciomercato claims that Kostic is up for sale as he has now fallen down the pecking order behind both Samuel Iling-Junior and Andrea Cambiaso.
Roma could rival West Ham for the signature of Kostic, who recorded 33 goals and 64 assists in 172 games for Eintracht Frankfurt between 2018 and 2022, winning the Europa League in his final season at the club.