The 41-year-old is believed to be one of the leading candidates to succeed Los Blancos boss Carlo Ancelotti, who is widely expected to take the Brazil national team job in the summer of 2024.
Ancelotti, 64, has won the La Liga title and Champions League since returning to Real Madrid in 2021 for a second stint in charge, and his current contract is due to expire at the end of this season.
Alonso, meanwhile, has spent almost a year in charge of Leverkusen, steering the Bundesliga club away from the relegation zone before securing a top-six finish last season as well as reaching the Europa League semi-finals.
Leverkusen have since made a bright start under the Spaniard this term, winning seven and drawing one of their opening eight games in all competitions, and they currently sit top of the Bundesliga table.
Alonso was linked with Premier League duo Tottenham Hotspur and Chelsea in the summer, and rumours over a possible exit from Leverkusen continue to circulate, with Real Madrid, Bayern Munich and Liverpool all believed to be monitoring his progress in Germany.
The Spaniard spent 13 years of his playing career across spells with Liverpool, Real Madrid and Bayern, including five years with Los Blancos between 2009 and 2014.
Ancelotti, who coached Alonso at both Real Madrid and Bayern, recently admitted that he would like to see the former midfielder manage Los Blancos in the future.
However, a switch to Spain in 2024 could prove challenging as Leverkusen chief Rolfes has insisted that Alonso is committed to working for the Bundesliga club.
Speaking to reporters, via Mundo Deportivo, Rolfes said: "We got his commitment a few weeks ago, when he extended his contract. Xabi doesn't have to say anything. He has extended his contract. He's fully focused here."
Alonso put pen to paper on a two-year contract extension with Leverkusen in August, keeping him tied to the BayArena until the summer of 2026.
Last week, the former Real Sociedad reserve coach refused to be drawn on speculation with the Real Madrid job, telling reporters: "It's too early to talk about this, we're in September, so it's not an issue to discuss.
"Both the players and I know how football works, it's not a problem for anyone, and we have not talked about it."
The likes of Zinedine Zidane, Raul and Alvaro Arbeloa, who also represented Real Madrid in their playing days, are among a number of others to have been linked with succeeding Ancelotti in the Los Blancos hotseat.