The former Manchester City, West Ham and Real Madrid boss will succeed Rubi, who was sacked by the La Liga outfit last week, as full-time coach.
Browsing: new manager
The report in El Pais said the Chilean, 66, has agreed to sign a two-year contract with the option of a third year with Betis, who sacked coach Rubi last month.
Boro are 21st in the Championship after losing 3-0 at home to Swansea City in their first game since the season restarted on Saturday.
Earlier this week, the struggling Championship outfit revealed that they had parted company with Jaap Stam but the Royals have wasted little time in securing a replacement.