As opposed to the Glasgow derby between Celtic and Rangers, the Edinburgh version usually provides little in the way of on-field incidents and Jefferies says this weekend's meeting will be no different.
"The police will probably say something, but I haven't seen anything in the recent derby games. The incident with Derek Riordan (who was sent off in the first derby of the season] was just petulance at Easter Road the last time. Nobody was sent off in the last game. There haven't been too many incidents," he said.
"I don't think anything has got out of hand at all. They've been hard, well-fought affairs and I'm not expecting anything else on Sunday."
Jefferies also touched on the Scottish Cup clash between the Hoops and 'Gers in early March which was all over the news for the wrong reasons.
"You remind the players of their responsibility. We know what's happened recently, but I maintain more was made of that than what it was," he added. "Some things were wrong in it, but it didn't get as out of hand as the attention it got.
"I don't see it as a major problem. We've just got to be wary that it's made everyone aware of the situation, so it's up to (Hibs boss) Colin (Calderwood) and I to put that message across: compete for every ball, but don't have any silly retaliations which can explode into things - and make sure the two men on the bench keep their cool.
"I heard Colin telling his players not to get involved in anything stupid and that's right - although we still want it to be competitive. These games are hard enough to win without going down to ten men."