'We have asked Andy Murray, through his agent, for a meeting as soon as possible to discuss the claims made public," an ATP spokesman said.
Earlier on Tuesday, Murray said players were aware that matches on the ATP Tour were being thrown.
"It is pretty disappointing for all the players, but everyone knows that it goes on," the Scot, who is in Moscow for the Kremlin Cup, told the BBC.
"It's difficult to prove. They can try their best until the last games in each set and then make some mistakes, hit a couple of double faults and that's it."
In order to crack down on such rumours, the ATP said players would have 48 hours to tell the governing body if they are approached to throw a match or risk punishment if they fail to do so.
Two weeks ago little-known Belgian Gilles Elseneer said he was offered 100,000 euros (70,000 pounds) to throw a first-round Wimbledon match in 2005 but the authorities were not aware of this incident until it hit the headlines last month.
"Nothing is more important than the integrity of our sport and the ATP has shown that it will act where it has information which requires investigation," the ATP spokesman added.
"Our Anti-Corruption Programme has stringent procedures in place to deal with any suspected corruption. It is the responsibility of everyone, without exception, to ensure we have any information about possible threats to the integrity of tennis. Tell us and we will act."
A new integrity unit is also being set up to counter the problem.
"The ATP Tour, Grand Slam Committee, ITF and WTA Tour see the establishment of a dedicated global Tennis Integrity Unit as a key priority for the sport and plans to create one are well advanced," ATP executive chairman Etienne de Villiers said in a statement.
"We have had a number of very constructive meetings on the issue this year and will be meeting again this week, with external experts, to discuss the next steps in ensuring a Unit becomes a reality as soon as possible."
The ITF oversee the running of the grand slams, the Davis Cup and Fed Cup competitions, while the WTA tour are the governing body of women's tennis.
