The 24-year-old is available for a move this month as he looks to play more regularly. He has made only two appearances for the English Championship side this season.
Hearts are interested in a loan deal until the end of the campign after losing another on-loan wide player, Josh Ginnelly, to injury.
Kastaneer is known as a quick and direct forward who can play on either flank or through the middle. At 6ft 1ins tall, he carries an additional physical presence. Several English teams have also declared an interest in loaning him this month.
Born in Rotterdam, he represented the Netherlands up to under-21 level before changing international allegiance to Curacao. He has won three caps for the Caribbean island so far.
Kastaneer played for Dordrecht, ADO Den Haag and FC Eindhoven in the Netherlands. He moved to German club Kaiserslautern in 2017 but was released a year later to join NAC Breda.
He signed a three-year contract at Coventry in 2019 but is currently on the fringes of the first team and wants more game time between now and the end of the campaign.
Kastaneer could be one of three new arrivals at Tynecastle Park before the transfer window closes at midnight tonight. Hearts are also in the market for a central midfielder and a right-back.
Striker Armand Gnanduillet and winger Gary Mackay-Steven have already been added to the squad since the window opened.
On what is expected to be a busy deadline day, the Edinburgh club are also looking to move a couple of players out.