Mourinho, who was sacked by United on Tuesday, spent three eventful years with Real between 2010 and 2013, winning the La Liga title with a record 100 points, scoring 121 goals, as well as lifting the Copa del Rey.
Yet his tenure also deeply divided the club's supporters and players, and Ramos was among the most outspoken of the Portuguese coach's critics.
Yet with Real still reeling from Zinedine Zidane's departure, having sacked his replacement Julen Lopetegui in October and then appointed the inexperienced Solari, some Spanish media reports have said president Florentino Perez could be tempted to bring Mourinho back.
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Head Coach Jose Mourinho of Real Madrid celebrates after the Copa del Rey final match between Real Madrid and Barcelona at Estadio Mestalla on April 20, 2011

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"Mourinho left us five years ago yet everyone keeps talking about him. People need to show more respect to the coach we have now," Ramos told a news conference ahead of the FIFA Club World Cup final against Al Ain on Saturday.
"I'm not the person who decides which coach comes here or doesn't, some people seem to think that the captains decide which coach Real Madrid appoints."
Victory over local side Al Ain in the Club World Cup final in Abu Dhabi would hand former Real midfielder Solari his first trophy as coach and see the club overtake Barcelona as the most successful team in the competition's history with four triumphs.

Santiago Solari

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Although Solari has led Real to 10 wins in 12 games since succeeding Lopetegui, the team have still faced plenty of criticism for some insipid recent performances.
They have fallen five points behind Barcelona in the La Liga title race but Ramos believes winning a trophy would offer the team an emotional boost.
"No-one can doubt the record of any one of us and we have another chance to defend the Club World Cup title," Ramos added.
"No-one has ever done this (win it four times), we are looking forward to the final with hope and we want to go home with the prize. It would be great for us on an emotional level to come back with the trophy."
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