The 21-year-old is part of the under-23 squad at Goodison Park and is available for a loan move this month.
Hearts have made an enquiry and talks are expected to continue over the coming days. The Edinburgh club are in the market for a forward after allowing Armand Gnanduillet to join Le Mans in France last week.
Simms made his Everton debut last month against Chelsea and is keen to play more regular first-team football.
With Beni Baningime having made a successful transition from Goodison to Tynecastle this season, the striker is interested in the prospect of following suit.
At 6ft 1ins tall, he is powerful, quick and a regular goalscorer for Everton in England’s Premier League 2. His contract on Merseyside runs until 2024.
Simms hit ten goals in 24 appearances while on loan at Blackpool during the second half of last season. That contribution helped the club achieve promotion to the Championship before he returned to his parent club.
Another loan move would supplement his experience of senior football and the Scottish top flight is a realistic destination.
As well as moving Gnanduillet on, Hearts also loaned Jamie Walker to Bradford City this month and are consequently short of attacking options.
Top goalscorer Liam Boyce returned from a calf injury to score his 12th and 13th goals of the campaign in Saturday’s Scottish Cup win at Auchinleck Talbot.
However, he needs help between now and May as Hearts look to qualify for European football for the first time in six years.