Two high-profile figures have never really seen eye-to-eye throughout their respective coaching careers and have regularly taken the opportunity to attack one another.
A war of words has intensified in the 2017-18 campaign, with Mourinho having accused Conte of behaving like “a clown” on the touchline , before the Italian hit back by advising his Portuguese rival to look at his own history of technical area theatrics .
The current United boss then brought up match-fixing allegations from the Chelsea coach’s past , with an unfortunate affair played out in public as verbal jousting became commonplace at pre and post-match press conferences.
Grant believes the petty arguments reflect badly on two men who should know better, with the former Chelsea boss telling Goal ahead of a rekindling of rivalries at Old Trafford on Sunday: “Nobody needs to say what they said.
“Football is a game of emotions and sometimes even coaches need to be good examples with things that they don't need to say.
“I'm sorry about this because they are two top managers and they have done this, but it will be settled on the pitch between the players of Manchester United and Chelsea. The coaches will not play.
“They are mature people and I'm sure that they don't want to fight with each other. They did what they did and they will finish with this. The only fight in football needs to be on the pitch.”
United and Chelsea are set to lock horns in Premier League battle with just three points separating them in the table.
Both sides head into that contest on the back of European stalemates in the first legs of their respective Champions League last-16 encounters.
Grant believes Conte’s side can take positives from that performance, despite conceding an away goal, and thinks that the Blues can still progress past the Catalans .
He added on a heavyweight encounter with Barca: “I think Chelsea played well. They did a lot of counter attacks. They hit the post twice.
“Barcelona is Barcelona. They know how to hold the ball. It doesn't matter which coach is in charge. The system is the same, they have the same identity, but I'm not sure if Barcelona will qualify.
“Chelsea can be a good counter-attacking team and like they did to Barcelona when they won the Champions League, they can do it again.
“Part of my job when I joined [Chelsea] as a director and then as a coach was to build a style of play, but it's difficult to build one style of play when the coaches are changing.
“On the other hand, even Real Madrid don't have a style of play - they change from time to time according to the players they have. I have a feeling that Chelsea will win in Barcelona.”