The Mirror says the 27-year-old centre-half has lifted the Portuguese title three times, in addition to winning the Europa League, the Portuguese Cup and the UEFA Super Cup.
Redknapp has already kicked-off his Loftus Road revolution by signing striker Loic Remy from Marseille.
He is also still in for Rennes midfielder Yann M’Vila too, and wants to continue revamping the spine of the Hoops side with Rolando.
But the player, who has 18 caps for Portugal, has already rejected a move to west London THREE times.
The first was a loan switch during Mark Hughes’ reign, the second after Redknapp arrived in November and the third is understood to have come this week.