But more research will be called for and some doubts remain.
The Stewart Inquiry has spent 10 months investigating claims that emissions from mobile phones damage the brain.
The inquiry, headed by Professor Sir William Stewart of Tayside University, is also expected to say some of the £22bn raised by the sale of mobile phone licences should be ploughed into further research.
The independent group, set up by the government, is believed to be in favour of restrictions on the siting of mobile phone masts.
The panel features experts in physics, telecommunications, engineering, neuroscience and radiobiology.
Alasdair Philips, of consumer watchdog Powerwatch, said: "Our understanding is that the report will state that, for the majority of people, reasonable mobile phone use should not cause any adverse health consequences, but that the jury is still out on possible links with a variety of effects including headaches, earaches, skin problems, concentration and short-term memory problems."
'Wholly inadequate'
He added: "What we believe they will say is that to date the government spending on mobile phone health effects has been wholly inadequate.
"They are recommending that a significant percentage of this licence money is allocated for further mobile phone research, particularly on mental functioning."
It is understood the group considered work from Poland on military personnel exposed to low levels of pulsed microwaves over a number of years, which led to a 14-fold increase in adult leukaemia.
Professor Stewart was not available for comment and the National Radiological Protection Board and the Department of Health declined to comment before publication of the report on May 11.
A spokesman for the Federation of the Electronics Industry said: "We have co-operated fully with the Independent Expert Group on Mobile Phones and look forward to reading its conclusions."
The Consumers' Association published research in April which showed hands-free kits - which had been promoted as a way of reducing microwave interference on the brain - could actually amplify the energy and channel it directly into the caller's head.
However, some scientists say there is no proof of a link between mobile phone use and damage to the brain.