The 28-year-old only made 11 appearances for Los Blancos during the 2021-22 campaign, managing just one goal and one assist during a frustrating campaign.
The striker struggled with injury problems during spells of the season, but he was involved in four of their final seven La Liga matches of the campaign.
Mariano did not feature in the Champions League final against Liverpool, though, and he is believed to have been told that he will again struggle for starts next term.
According to Marca, the centre-forward has made it clear to Real Madrid that he wants to leave the club during this summer's transfer window.
Mariano still has another 12 months left to run on his contract at Bernabeu, having penned a five-year deal with the club upon his return from Lyon in August 2018.
The Dominican Republic international initially represented Los Blancos between 2012 and 2017 before joining Lyon, scoring 21 times in 48 appearances during a successful spell with the French outfit.
Mariano returned to Bernabeu in 2018 but has only managed seven goals in 59 appearances during his second spell at the club, including only six goals in 44 La Liga outings.
The report also claims that Luka Jovic is set to depart, with Fiorentina believed to be in talks over a potential loan deal for the Serbia international.
The 24-year-old has scored three times and registered five assists in 51 appearances for Real Madrid, including just one goal and three assists during the 2021-22 campaign.
Vinicius Junior, Karim Benzema, Eden Hazard and Rodrygo will all definitely be at Bernabeu next season, but Gareth Bale has left on a free transfer, while Mariano and Jovic could soon depart.
Los Blancos are not believed to be actively looking to sign a new attacker this summer, although they were prepared to pay Kylian Mbappe a huge salary and signing-on fee before the France international decided to sign a new deal at Paris Saint-Germain.
Aurelien Tchouameni and Antonio Rudiger have arrived at the club this summer, and club president Florentino Perez recently said that there were unlikely to be any further signings.
However, exits for Mariano and Jovic would leave head coach Carlo Ancelotti short of options in the final third, especially as Isco has also departed on a free transfer ahead of next season.