The Spanish striker is out of contract at Schalke at the end of the season, and with a contract yet to be agreed, the former Real Madrid man could leave the Veltins Arena.
Raul, who lives in Dusseldorf, has previously come out as a supporter of Fortuna and previously joked he would love to play for his local side as he could cycle to training.
The president of the 2.Bundesliga club, Peter Frymuth, would like to bring Raul to the Esprit Arena and joked to Express: "I've heard of delays in Schalke because he wants to see our situation."
Fortuna are currently third in Germany's second tier, and despite promotion appearing to be on the cards, it is unknown whether the club could realistically afford to sign the 34-year-old.
However, if the striker was to join his local outfit, he would not be the only Spaniard at the club after Juanan signed last summer, and Frymuth quipped: "We are currently considering whether the two could play together."
Raul is set to be in Bundesliga action on Sunday when Schalke entertain Hannover, with both teams looking to shrug off their Europa League hangovers.