The Sun says Inter are bankrolled by billionaire oil magnate Massimo Moratti and are prepared to match the huge £24 million fee Chelsea splashed to land Essien from Lyon three years ago.
The Premier League runners-up are expected to put up a fierce fight to keep their big names.
But Mourinho wants Essien to be his midfield enforcer at the San Siro while the Ghana star would love to be reunited with his old boss.