The Spanish striker has yet to commit his future to the Bundesliga club, and the impasse in negotiations over a new contract has alerted the Qatari outfit
The 34-year-old's contract with Schalke expires at the end of the season and he has not yet reached an agreement with the Bundesliga club over an extension.
The Spaniard is hoping for a two-year deal, but the German side have only offered him a 12-month deal, which he has yet to accept or reject.
Al Rayyan have reportedly contacted former Spain international Fernando Hierro, who played at the Qatari club in 2003-04, in order to persuade Raul to take up a challenge in the Persian Gulf.
Schalke sporting director Horst Heldt is not intimidated by the interest from Al Rayyan, however, saying: "I would be very surprised if he moves to Qatar.
"For him it is not about the money or how long his contract will run. This is about his life plan."
Raul, who joined Schalke in 2010, has scored 20 goals in all competitions this season and has previously revealed that he is comfortable and settled in Dusseldorf. However, he would have to take a substantial pay cut from his current €7 million wages, as Schalke have pledged an estimated €3-4m in their new offer.
Earlier in April, the former Real Madrid man admitted that he would only decide his future after talking to his family.