Rodriguez left Real Madrid for Bayern Munich last summer, signing a two-year loan deal with the Bundesliga giants.
The Colombia international chose to quit the Bernabeu for a new challenge elsewhere, having tumbled down Zinedine Zidane’s pecking order.
A Real Madrid return, however, has been mooted with reports suggesting new manager Lopetegui is a huge admirer of Rodriguez.
And Spanish newspaper Marca claim the Spaniard has reached out to Rodriguez in the wake of succeeding Zidane.
It is said he told the Bayern star he would love to have him in his squad, particularly after Cristiano Ronaldo’s exit.
Marca say, though, that Rodriguez will not be returning.
He intends to honour his agreement with Bayern by staying at the Allianz Arena this season, where the club are preparing for a new era under Niko Kovac.
However, Rodriguez supposedly has his heart set on a return to Real in 2019.
Bayern have an agreement with Real that allows them to sign Rodriguez when his loan deal expires.
But the Colombia star feels that, if he intervenes, Bayern will have no choice but to accept his wish.
Rodriguez recently expressed his satisfaction with life in Germany, saying: “So far, I’m still here and I’ve had a spectacular first season.
“I’m very happy there and I feel like the club and the fans love me very much.”
And new Bayern boss Koac added: “We have a loan deal which is 100 per cent valid. It will only end if we want to. He’s going to stay here.”