The Sunday Telegraph newspaper said the troops would be based in British-controlled areas in southern Iraq but could also be moved to more dangerous areas nearer Baghdad if Prime Minister Tony Blair gives his approval.
The fresh deployment would increase the number of British troops in the country to in excess of 9000.
A Ministry of Defence spokesman said any announcement would be made to parliament.
"We have always said we would be prepared to send more troops to Iraq if necessary during the election," he added.
Washington has already announced it will deploy an extra 12,000 troops to bolster security for the election, increasing its troop numbers to 150,000.