Yesterday evening, the two men almost came to blows live on Sky News while they discussed the way forward for British politics in the current state of hung parliament.
After Campbell claimed Boulton was "clearly upset that David Cameron is not prime minister", the Sky News journalist angrily warned him not to dictate "what I think".
Following the argument, Sky said: "Sky News political editor Adam Boulton defended his integrity and, by implication, Sky News's, against an attack by Alastair Campbell."
However, Ofcom received several hundred complaints from viewers, mostly about the unprofessional way Boulton lost his temper.
A spokesperson for the watchdog said: "We need to make an initial assessment to see if there is a case to answer."
Ofcom has also received a number of complaints about Boulton's interview with Labour culture minister Ben Bradshaw later in the same evening, when he again appeared to lose his composure.
The exact number of complaints for each transmission will be published tomorrow when the media regulator releases its weekly broadcast complaints report.
Ofcom is already assessing around 700 complaints about Boulton's alleged "heckling" of Liberal Democrat leader Nick Clegg during the Sky News prime ministerial debate in April.