Research carried out by the regulator over a month found that four out of five consumers received nuisance calls, averaging two a week.
A quarter of people who took part reported receiving more than 10 nuisance calls over the period. Those who took part in the survey were designed to reflect the general UK population and they were asked to make a diary of the calls they received.
The bulk of nuisance calls related to payment protection insurance (PPI), which made up more than half (51%) of unwanted sales calls.
Ofcom said complaints figures have indicated that large numbers of nuisance calls are being generated by some claims management companies.
A spokeswoman for Ofcom said the regulator is gathering further evidence and if its suspicions are confirmed it will launch full-blown formal investigations against these firms.
Ofcom has also written to the Ministry of Justice (MoJ) to draw attention to the extent to which PPI claims appear to be driving nuisance calls.
Calls about PPI were considered to be the most "annoying" by more than 850 people surveyed while calls from companies purporting to offer computer support or maintenance were seen as the most "worrying" and "distressing".
Energy, market research and insurance were also among the most commonly cited reasons for unwanted calls. Consumers were only able to identify the name of the company calling in one in five nuisance calls and the telephone number in one third of these calls.