He is set to start in the final as Real aim to win the tournament for the fourth time in five years.
And Liverpool, Diario Gol say, are keen to make him their No 1 for next term.
It is said Real were mulling over whether to include him in a potential deal for Mohamed Salah, who is valued at £200million.
However, Liverpool are likelier to pursue a deal separately instead.
Meanwhile, speaking after last night’s 2-2 draw with Bayern, Navas expressed his delight at reaching yet another final.
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Liverpool transfer news: Jurgen Klopp is eyeing a deal for Real Madrid's Keylor Navas
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"We are making history - the team never lets its hands down, keeps fighting until the end," Navas said.
"We will prepare well as we must, with all the motivation, respecting the opponent we get, but very much wanting to win."
Liverpool are not the only club to have been linked with Navas.
The Real Madrid star nearly joined Manchester United in the summer of 2015 after an agreement was reached.
However, a faulty fax machine saw him instead remain at the Bernabeu, with David De Gea’s move to Real also falling through.