Former Manchester United manager is the favourite to take over following Sunday's clash with Real Valladolid and is likely to be named manager through until the end of the season, goal.com reported.
Real Madrid executives, headed by Florentino Perez and Jose Angel Sanchez, held a four-hour meeting on Thursday where they decided that Mourinho will be an option to be the club's coach until the end of the season, with it also decided that Sunday's match against Valladolid will be Solari's final game in charge.
The call to sack Solari – who only replaced Julen Lopetegui in October – came in the aftermath of Madrid's shocking Champions League defeat at the hands of Ajax on Tuesday evening, though they have spent the past 48 hours discussing whether to keep the Argentine in charge for the remainder of the campaign.
The hiring of Mourinho will not be on a fulltime basis however, with Madrid still hoping to convince Zinedine Zidane to return to the club's bench for next season.
Madrid would like to bring Zidane back now, but the French manager is not convinced he is in a position to step back in immediately, hoping instead to be available at the end of June.
Mourinho has been far more receptive to approaches from the Spanish giant, both in public and in private, making him the most likely option to take over for the closing run of the Liga season.
Real believes a change must be made to stop the bleeding following a week that saw the club knocked out of the Copa del Rey and the Champions League, along with losing a home Clasico to fall 12 points behind leader Barcelona in La Liga.
Mourinho and Zidane were joined by Germany boss Joachim Low on the list of possible managers club executives discussed on Thursday as potential fulltime replacements though, like Zidane, it is understood that Low would not be available until the end of June.
With the change set to take place on Monday, the new manager will have just one week of training before facing Celta Vigo, though Real would then have the benefit of an international break to try and find some answers for the club as it heads into the final 10 matches of the season.
Los Blancos currently sit third in the table, five points behind second-placed Atletico Madrid and six clear of fourth-placed Getafe.