"It is a sign of attachment to the club and a spirit to always win," added the statement.
The Portuguese said on Saturday that "little things" were needed to make him stay at the San Siro, hinting at a desire to strengthen his squad after an early exit from the Champions League this season.
Inter have won Serie A for the last four seasons, but have struggled to make an impact in Europe with defeat by Manchester United in the first knockout stage in March marking their latest failure.
However Mourinho's record of success at the top level - winning the league in Italy, Portugal and England, as well as the Champions League - means he is frequently linked with other clubs.
In February, he said he would like to return to the Premier League with Chelsea at some point in the future, while he is one of the names mentioned as a possible successor for Sir Alex Ferguson at Manchester United in the future.
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