Marco Villiger, head of legal affairs at world football's ruling body FIFA, and Gianni Infantino, general secretary of European counterparts UEFA, expressed concern over betting on things like the next free kick, throw-in or yellow card.
"These live bets are a problem," said Villiger on Friday at a conference on early warning systems designed to alert footballauthorities to irregular betting patterns and possible match-fixing.
"It's very easy to manipulate if you contact a player and tell him to kick the ball into touch at the start.
"You would be able to bet on that and it would be difficult to decide if it is an irregular bet or not. We will have to think about whether we should continue to offer such live bets," added Villiger.
Infantino said the football authorities were planning talks with the betting operators.
"This is something we want to address and the next discussion we will have is with the betting operators," he told reporters.
"It's something we haven't focused on too much since we were always focusing on [the fixing of] the result, then you realise it switches much more from the result to the live betting."
UEFA president Michel Platini has described match-fixing as the biggest scourge facing the sport.
European football's governing body monitors 29,000 matches a year - including under-21 internationals, Europa League qualifiers and second division fixtures - for irregular betting which could indicate a game has been fixed.
ANTALYA PROBE
FIFA is investigating two friendly internationals played in the Turkish resort of Antalya last month - Latvia v Bolivia and Estonia v Bulgaria - where a total of seven penalties were awarded, one of which was taken twice when the first effort was saved.
"The criminal organisations are getting around the measures we introduced because the early warning system works for the results," said Infantino.
"This [in-game betting] is much more difficult to monitor. This is people betting on the next goal, the next throw-in, the next yellow card.
"This is something you can easily do, you don't have to do anything serious to get a yellow card, you can just trip somebody, throw the ball away, time-waste, it's really easy to do," added Infantino.
Friedrich Stickler, president of the European Lotteries Association, agreed in-game betting needed to be carefully controlled.
"In my view it's dangerous," he said. "When you kick the ball out or when you make a small foul to get a yellow card this does not affect the game.
"He might become hooked to the criminals so this is a door which opens to criminal activities.
"When you start with little things, one day the same guy might tell the player to give away a penalty. I think we should sit together, the associations and sports betting organisers, to discuss what bets should be accepted," Stickler added.
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