The demand is a direct challenge to the Swedish Trade Union Confederation (Landsorganisationen - LO) which considers unemployment insurance (arbetslöshetsförsäkring - A kassa) to be a union matter.
"It's highly illogical that it is under union management, all the other social security insurances are state," Björklund said to the Dagens Nyheter daily.
Björklund pointed out that the state currently meets two-thirds of the costs of unemployment insurance schemes.
The demand, which the party executive will consider at the weekend, is therefore likely to become an election issue.
The government, of which the Liberal Party is a member, recently set up a parliamentary inquiry into sickness and unemployment insurance, which is scheduled for completion by 2013. The Liberal Party has now indicated that it is reluctant to wait.
LO chief Wanja Lundby-Wedin has described the move an attack on the Swedish model. The unions want to retain control over the unemployment schemes as it means that most of those working in Sweden are obliged to join and thus become members of the union.
Björklund however dismisses this line of argument and states that Sweden has along and established tradition of union membership.
"I do not think the unions need to be worried, adding that he supports the collective bargaining model between strong partners in the labour market, while social insurances, except currently unemployment insurance funds, are matters for the state."