Toffees striker Andrew Johnson is expected to be out of action with an ankle injury, leaving them short up front.
Healy, 27, has emerged as a target for them, either on loan or permanent , if Leeds are prepared to accept £500k.
Everton boss David Moyes knows all about the Northern Ireland forward, having taken him to Preston North End six years ago, when he spent £1.5m to buy him from Manchester United after a short loan spell in January 2001.