Reports in Spain suggested Real were closing in on a deal for the France forward, while Goal understands Manchester City are also in talks to sign the young star.
Raul, who was the club's record goalscorer before being usurped by Cristiano Ronaldo, is unsure whether a deal will happen but says nothing should be ruled out until the transfer market closes.
Speaking to Marca, the former Spain striker said: "The market will set the price. There has to be an agreement between several parties and that will define it.
"Real Madrid have great players but it is clear that until August 31, anything can happen. For now you have to focus on those who are here and we'll see what happens."
Despite having yet to acquire Mbappe, Madrid allowed Alvaro Morata to leave for Chelsea with the Spain striker having grown frustrated at a lack of playing time.
But Raul does not believe it is imperative for Zinedine Zidane to buy another forward before the new season begins.
"Morata was a very important player for the club and for the team. He scored a lot of goals but now he's at Chelsea," he added.
"We'll see what there may be on the market, but I think we already have world-class strikers who can score goals."