The Brazil superstar has been linked to the Spanish giants, as well as former club Barcelona, and he was absent as Paris Saint-Germain opened their Ligue 1 title defence with a 3-0 win over Nimes on Sunday.
Madrid are prepared to swoop in with a bid in excess of €100 million (£92m/$112m) for him, though Goal understands Barca could convince PSG to sell with an offer of €50m plus Philippe Coutinho and Nelson Semedo .
PSG's sporting director Leonardo hinted Neymar could be close to leaving the French capital, saying negotiations over his exit were "more advanced" but says no agreement has been made .
Madrid have already signed Eden Hazard from Chelsea during the off-season and Hagi – who played for Los Blancos between 1990 and 1992 – says the addition of Neymar would make them a formidable force in the 2019-20 campaign.
"They can win easier," he told Super Deportivo Radio . "Without a doubt. If they sign Neymar and with the Hazard signing, they can win the Champions League again.
"[Zinedine] Zidane will then have to find a place for each one, but it's the best thing that can happen to a coach. You just have to motivate them."
"There are times that he is good and sometimes he is not," he added. "The value of the player is the same. He is a player who would do well for all the teams in the world."
Hagi was also drawn on the age-old debate of whether he prefers Lionel Messi or Cristiano Ronaldo, with the 54-year-old opting for the Barca star.
"I would love to be his coach, but I confess that I choose Messi because I have a small weakness for him being left-footed," he explained.
"I was a left-footed footballer myself. I can't choose another one, it's my style."