Maignan, 29, only has a contract at San Siro until June 2026, but there are currently no indications that the goalkeeper is close to penning an extension with the Italian giants.
According to Fichajes, Real Madrid are attentive to the situation, with Los Blancos long-term admirers of the Frenchman, who is viewed as a potential replacement for Thibaut Courtois.
The report claims that Maignan wants an annual salary of between €7m (£5.9m) and €8m (£6.8m), which represents a big rise on his current €5.5m (£4.6m) wages.
Milan are not believed to be willing to go to that number, creating a potential stand-off, with Maignan potentially leaving the Italian giants in the not too distant future.
Real Madrid 'interested' in Milan goalkeeper Maignan
Maignan started his professional career at Paris Saint-Germain, but he failed to make a first-team appearance for the capital giants before moving to Lille in 2015.
The goalkeeper featured on 180 occasions for the French outfit before arriving at Milan, where he has featured 113 times over the last four seasons.
Maignan has won the Serie A title during his time at San Siro, but he has entered the final 18 months of his contract, and it remains to be seen whether he pens a new long-term deal.
Real Madrid have one of the best goalkeepers in the world between their sticks, with Courtois seemingly fully overcoming the serious knee injury that forced him to miss most of last season.
Could Maignan replace Courtois?
Courtois has a contract at Bernabeu until June 2026, and there is no question that he is still one of the best goalkeepers in the world, so a change in that area at this stage would be a huge surprise.
The Belgian will be 33 by the end of last season, though, and there is a chance that he could decide to leave at the end of his current deal, with a move to Saudi Arabia a possibility.
Maignan could decide to spend another two seasons at Milan before leaving on a free transfer in 2026, with the Frenchman potentially arriving as a replacement for Courtois.
However, if a deal could be done a year early, then the Frenchman could potentially battle Courtois for the gloves during the 2025-26 campaign.
Real Madrid are also believed to be interested in Brighton & Hove Albion's Bart Verbruggen, with a new goalkeeper seemingly viewed as a priority for the club next year.