Mourinho spoke this week in Spain and revealed he would welcome an eventual return to Stamford Bridge and added he felt "nothing" for his successor, although Grant was diplomatic with his response.
He stressed he had the utmost respect for Mourinho's work for the club - bringing consecutive Premier League titles, the League Cup twice and the FA Cup - but is focused on the future rather than the past.
"I have respect for what Jose did at the club in the past," he said. "The club brought me here to go a different way and that's what I have to concentrate on.
"I'm not a man of fighting. I'll only fight for my team on the pitch, do everything for my club, and I have a lot of respect for all people, including Jose. I have no problem with him."