Media in Italy raised the possibility based on Mourinho's decision to register his two children at the schools they attended while he was coaching the club he led to the Seria A, Italian Cup and Champions League titles last season.
Tackled on the rumours Mourinho told a press conference: "What they're saying each day in Italy that I will once again be coach of Inter next season is false, completely false."
He added: "I am more and more content and happy at Real Madrid...normally my teams are always better the second season than the first. Because of that I want to be here next season, with the belief that Real Madrid will be better."
Mourinho was speaking in the aftermath of Wednesday's 1-0 extra time Spanish Cup final win over Barcelona, their bitter rivals waiting for them in the Champions Lewague semi-finals.