According to Marca, Bernebeu chiefs are keen on adding some firepower to assist Karim Benzema up front and Neymar is on top of their wish-list.
Earlier this month, there were reports that Real were weighing-up a world record bid for the 27-year-old and were set to offer him wages of £40million over five seasons to make him the highest earner in football.
Neymar has long been on the radar of the La Liga giants and president Florentino Perez is still keen on luring him to the Spanish capital.
The report also states that Real are still interested in signing Eintracht Frankfurt striker Luka Jovic too.
Jovic has been a revelation in the Bundesliga this term, netting 17 goals in 27 league matches.
However, Los Blancos chiefs want to make one major signing as Cristiano Ronaldo was never replaced with a big name at Madrid following his £100million summer switch to Juventus.
Signing Neymar would be the big statement the club will want to make.
The forward reportedly does not feel settled in Paris and may consider his future at the club after they were knocked out of the Champions League to Manchester United last month.
PSG may not be able to resist an offer of such magnitude amid Financial Fair Play concerns with UEFA still to decide on whether to investigate alleged breaches.
Source: Daily Post