The current Liga champions are long-term admirers of Bale's and Goal.com revealed in December that the north London club are already preparing for his potential exit in the summer.
And Reina believes that Bale is comparable to Liverpool talisman, Luis Suarez, who has also been linked with a move to Spain, although the keeper does not expect the Uruguay man to leave Anfield.
He told Marca: "If Real Madrid signs Bale I'll be delighted. He causes me a lot of problems!
|66/1||Gareth Bale is 66/1 with Paddy Power to score a hat-trick for Tottenham against Lyon
The shot-stopper also backed Real Madrid to beat Manchester United in their Champions League second-leg clash in two weeks after a 1-1 draw at the Bernabeu on Wednesday.
"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 are keen admirers in the Spaniard, while he has also been linked with a return to Barcelona to fill in for Victor Valdes, who has announced that he will leave the club when his contract expires at the end of next season.
"I'm sure Victor Valdes will have his reasons for deciding to leave Barcelona," the Reds man opined. "I respect him. He's my team-mate 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."