The Werder Bremen defender only signed for the club in January.
The report claims that Everton are keen on the centre-back, even though he only recently signed for Bremen from Hoffenheim.
The 22-year-old only joined up with his new team in January and has impressed since making the move to the Weser Stadion.
His current deal runs until 2018 and Bremen are of course reluctant to sell. However, the report claims they are not in the financial position to reject any proposal from Everton.
The Toffees are believed to be willing to spend up to €10 million on the player, to help put an end to their central-defensive issues.
Everton need support for John Stones and Phil Jagielka at the heart of defence. Sylvain Distin and Antolin Alcaraz are both out of contract in the summer and both have had poor seasons at Goodison. Most Everton fans would like to see at least one of them replaced.
Vestergaard then appears to have emerged as the number one target to do just that.