New CAP guidance on gambling ads, in effect since April, stipulates that offers should not be presented in such a way that creates an unjustifiable sense of urgency.
A spokesman confirmed the ASA is "carefully assessing several complaints" about ads from the three bookmakers to establish if they went against that guidance.
However, the watchdog is not investigating the other objections which accounted for the majority of the 115 complaints it received during the World Cup, which ran for a month from the middle of June on commercial broadcaster ITV as well as the ad-free BBC.
These other objections were about the volume of ads, which the ASA does not regulate, and about their scheduling when large numbers of children were watching. However, guidance preventing ads from running in programming that is aimed at children does not apply to World Cup games.
The ASA is set to publish further guidance focusing on the protection of children and young people later this year.
The watchdog tends to receive more complaints about gambling ads during major sporting events and this was true with the World Cup, which attracted five times the number of complaints than it received during the month before the tournament.