Joining the club from Mallorca in 2015, Asensio has made 91 appearances for Real Madrid following a year's loan deal to Espanyol at the start of his spell.
According to Sergio Santos Chozas of AS, while there have been recent rumours about interest in the player from Liverpool, there is no chance of the Spain worldwide departing the Santiago Bernabeu any time soon.
Liverpool have not submitted an official bid for the winger yet, but there is talk of the Anfield side readying a "mammoth bid" for the Spain global. But having failed to nail down a regular place in Zinedine Zidane's starting line-up last season, speculation has been growing that the 22-year-old attacking midfielder could be heading for the exit.
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Nabil Fekir will be offered a new contract if he rejects interest from Liverpool to stay at Lyon.
Liverpool have been linked with a move for Asensio during the summer transfer window as the Reds look to build on last season, which saw them reach the Champions League final but ultimately finish without silverware. Mundo Deportivo have claimed that the Anfield outfit are preparing a €180m proposal.
Another Los Blancos star who would fit the bill much better is Marco Asensio, someone that Sport says could be sold this summer in order to allow Neymar to be signed from Paris Saint-Germain.
Fekir, who scored 23 goals for Lyon last season and is part of France's World Cup squad in Russian Federation, had been identified as a long-term replacement for Philippe Coutinho by Liverpool.