The Brazilian stopper has emerged as one of Europe’s top goalkeepers this season and Liverpool have identified the 25-year-old as their long-term number one.
Madrid are keen on replacing Keylor Navas and are interested in Premier League duo David De Gea and Thibaut Courtois.
However, Zinedine Zidane’s side have a strong interest in Alisson and the Brazilian’s talked up a move to the Bernabeu.
‘Those links massage the ego, it cannot be denied,’ Alisson told Globoesporte.
‘People get satisfaction from having recognition. I feel very happy to have that recognition.
‘It means that I am doing my job well, that they are watching me.
‘Even more so when one hears about Real Madrid.’
More: Liverpool FC
Loris Karius has replaced Simon Mignolet as Liverpool’s number one goalkeeper in recent weeks but Jurgen Klopp wants a new stopper this summer.
A new acquisition is likely to signal the end of Mignolet’s time at the club as he seeks first-team football.