The Portuguese coach has come under fire from supporters this season following Madrid's slow start to the domestic season which has enabled arch-rivals Barcelona to establish an 11-point lead over Mourinho's men.
They are also five points behind second-placed Atletico Madrid despite Saturday night's 2-0 defeat of their near-neighbours.
Mourinho was jeered by sections of the crowd in last Tuesday's Copa del Rey defeat of Alcoyano, prompting the former Porto, Chelsea and Inter Milan boss to offer supporters the chance to vent their frustration by arranging to come to the side of the pitch 40 minutes before the Atletico game.
The reaction was mixed but with less than 5,000 fans inside the Bernabeu at the time, it offered little indication as to how the majority were feeling.
Nevertheless, it is now being speculated that Mourinho and Madrid president Florentino Perez have agreed his tenure at the club will come to an end next summer.
Under a picture of a broken heart, the Marca report claims: "Jose Mourinho will not coach Real Madrid next season. Both Mou and Florentino Perez believe the Portuguese's cycle on the bench at the Bernabeu is exhausted and that the current situation cannot continue beyond June 30."
Marca, who are known to have strong links with Real, report Perez has become concerned by a number of incidents this season which have not cast the club in a good light.
Firstly, there was an incident with Sergio Ramos which saw the Spain defender put on Mesut Ozil's shirt underneath his own after the German was substituted at half-time of a game against Deportivo La Coruna.
Ramos later claimed he was merely showing support for his team-mate but the move was perceived as an attempt to undermine Mourinho's authority.
Ramos was later dropped.
There was also the public spat with Alberto Toril, boss of the reserve side Real Madrid Castilla, who play in the Segunda Division.
Mourinho accused Toril of focusing too much on results rather than trying to produce young players for the first team.
And it would seem the publicity stunt prior to the Atletico game may have been the final straw.
Marca's report added: "Florentino believes Mourinho is 'committing suicide' with his decisions and statements this season - the Ramos case, the war with Toril and checking the pulse of the Bernabeu.
"They will try to get to the end of the season in a friendly manner as Florentino does not want a crisis in the middle of the season.
"But what is certain is that the decision is taken: this will be the last season of the Mou tenure in Madrid."
The speculation is sure to alert a number of clubs around Europe and, in particular, England where Mourinho is still highly regarded following his spell at Stamford Bridge where he won two Premier League crowns and one FA Cup.
He has been linked with a return to Chelsea, currently under the interim stewardship of Rafael Benitez, and Manchester United when Sir Alex Ferguson finally retires.
Mourinho joined Chelsea after leading Porto to a surprise Champions League triumph in 2004 and remained for three years.
He then joined Inter Milan and guided the Nerazzurri to back-to-back Serie A titles.
In addition to the Scudetto, Inter also landed the Coppa Italia and the Champions League in 2010 and in doing so became the first Italian side to win the treble.
A move to Madrid ensued and after winning the Copa del Rey in his first season in charge he ended Barca's stranglehold on the Primera Division crown last season.