The current Liga champions are long-term admirers of Bale, and Reina believes that he is comparable to Liverpool talisman Luis Suarez, who has also been linked with a move to Spain, although the keeper does not believe the Uruguay man will leave Anfield.
He told Marca: "If Real Madrid signs Bale I'll be delighted. He causes me a lot of problems!
"I can't see Luis Suarez playing in La Liga. I think he'll stay at Liverpool. He's a great player. So are Bale and a few others in the Premier League."
The shot-stopper also backed Real Madrid to beat Manchester United in its Champions League second-leg clash in two weeks after a 1-1 draw at the Bernabeu last week.
"I want Real to win the Champions League tie against United," Reina added. "It's a Spanish team and I've got lots of friends there."
Reina himself has been linked with a move from Liverpool. Arsenal is a keen admirer in the Spaniard, while he has also been linked with a return to Barcelona to fill in for Victor Valdes, who has announced he will leave the club when his contract expires at the end of next season.
He said: "I'm sure Victor Valdes will have his reasons for deciding to leave Barcelona. I respect him. He's my teammate and friend.
"He'll be leaving with his head held high, as he's given his all to Barcelona. Any talk of me joining Barca is just speculation. I've got a contract at Liverpool and I'm very happy here."