Karanka was assistant coach under Mourinho at Real Madrid and left the Spanish club around the same time as the Portuguese returned to Chelsea.
But instead of staying with Mourinho and heading to Stamford Bridge, Karanka went his own way and eventually replaced Tony Mowbray at Middlesbrough last month.
"I arrived at (Real Madrid) training one day and he (Mourinho) kept looking over at me. Suddenly he asked why I wasn't responding to his text messages," Karanka told La Sexta's 'Jugones' programme.
"I looked at my phone and there was a message from him asking 'if I go to (Chelsea) would you like to come with me?'
"At first, I was all for it but later I thought about it and decided against it as it was another league, another country."
Karanka must have changed his mind regarding moving to England as he joined Middlesbrough in the Championship on November 13 and the 40-year-old has led the club to one win from three games in charge.
The Spaniard credits Mourinho for teaching him a lot about being a head coach.
"With Mourinho every minute is a learning experience," Karanka said
"He is always three or four steps ahead, like during the (Champions League) match (last season) at Old Trafford when Nani was sent off and he immediately brought on Modric."
