Reports suggest the Foxes have been monitoring the midfielder for some time and could now be poised to make a move for his signature.
According to the Daily Mail, the Foxes have been closely monitoring the progress of the 21-year-old who has also caught the attention of Southampton and West Bromwich Albion.
Vilhena, whose contract with the 14-time Eredivisie winners runs out in the summer, has made 25 appearances this season, scoring five goals in the process.
He initially looked poised to join former boss Ronald Koeman at Southampton earlier in the season.
After a January move to St Mary's collapsed, Southampton allegedly held "secret talks" with the player last month, sparking speculation that a deal was close.
However, Leicester, who also reportedly considered making an approach in January, now look set to hijack the move, with their pending Champions League campaign seemingly making them a more attractive proposition.
But a move to the Premier League still may not be a foregone conclusion, with Feyenoord coach Giovanni van Bronckhorst recently hinting he is hopeful of tying Vilhena down to a new contract at De Kuip.