Don Balon says a decision has already been made: Zinedine Zidane will be asked for his resignation in June.
Perez knows the German is frustrated over losing his best players consistently at Anfield and can offer him the platform to build a team to his liking.
The Real president believes Klopp's personality and man-management is similar to Jose Mourinho and thinks the German is capable of making an instant impact should he take charge.
Klopp penned a long-term deal with Liverpool last summer and has always pledged his commitment to the Reds. But comments made last week were encouraging for Perez.
"I think if you lose your best player there's no way you can dress it up as a positive window, certainly in January as well," he said. "I think every Liverpool fan, myself included, when Philippe Coutinho stayed in the summer, felt okay.
"We know he's going next season, let's enjoy these 12 months, probably similar to Ronaldo, Luis Suarez, you always felt that was going to happen.
"To lose him mid-season, you know I don't agree. Philippe Coutinho is not worth that [£146m], he's not that good. I would have took £20m, £30m less in the summer to know that Liverpool would have had him in the second half of the season, because at that time we're still in the FA Cup, we're still in the Champion League."