A report claims the Toffees will have £100 million to spend this summer.
Strootman in action for Roma against Sassuolo
New Blues boss Ronald Koeman has been handed a £100 million transfer kitty, plus any money he rakes in from player sales, and will look to strengthen his side's midfield, the report claims.
Koeman's appointment was confirmed on Tuesday
A move for Zenit St Petersburg's Axel Witsel was mooted this week, and Strootman is said to have followed the Belgian onto Koeman's ambitious shopping list.
The 26-year-old, a perennial Manchester United target under Louis van Gaal, has suffered an injury hit two seasons, making just 12 first team appearances in that time.
Roma's Strootman holds his head in his hands
Despite this, the report claims Roma would be looking for a transfer fee in the region of £30 million, with Strootman having two years still to run on his contract.
Landing the former PSV Eindhoven man would be something of a coup for Everton, who unlike the Roman side will not be involved in next season's Champions League.
Should Strootman complete a move to Goodison Park, he'd be joining James McCarthy, Gareth Barry, Tom Cleverley, Mo Besic and Darron Gibson in the Toffees' engine room.
Strootman in action for Holland against Italy