At present there is little or no coordination between different parts of the country, so police or stewards in one region do not necessarily know if a supporter has been banned from all grounds in Sweden. A national database of hooligans could make this easier to enforce.
Eriksson, a former National Police Commissioner, handed over the first of his recommendations to the government this morning.
He also produced plans for who pays for policing at stadiums, which is a complex issue in Sweden.
"It’s unreasonable that clubs that are run as companies should pay for police surveillance around the arenas," he wrote in a debate article in Dagens Nyheter newspaper today.
"The costs should be covered by public means, as long as the company is owned by a non-profit organization of at least 51 percent. In that case, for example Djurgården (Idrotts AB) should not have to pay for policing, just like the non-profit IFK Göteborg.
Football hooliganism has blighted the domestic game in Sweden in recent years and has also crept into hockey.
The plans announced today mirror those in England introduced many years ago to combat the so called "English disease."
The chairman of the Swedish Football Supporters Union, Victor Capel, told news agency TT that he was positive to the introduction of a national hooligan register.
"The register can help today's legislation a great deal. At the same time, one must remember that it concerns people who have not been sentenced for a crime and one must be careful with how one uses it," Capel told TT.