Lloyds Banking Group could be forced to sell off its Halifax business if the European Commission decides to punish it for receiving billions of pounds of state aid, according to reports.Competition Commissioner, Neelie Kroes, has yet to make a final decision, but banking sources say it is clear that she is planning to impose draconian penalties on Lloyds, says the Times.It's thought Kroes has rejected Lloyds' attempt to limit the remedial action it must take to selling Cheltenham & Gloucester and making limited disposals in Scotland.The aim is really to force Lloyds, the UK's largest retail bank, with almost one third of the market, to relinquish a bigger chunk of its empire.'The Commission has not made a final decision, but what they are talking about Lloyds giving up sounds a lot like Halifax,' said a source close to the negotiations with Brussels.Another said the Commission feels it mustn't be seen to let the UK off lightly. But some say a compromise allowing Lloyds to keep the Halifax name but sell a large number of its 1,000 branches could be reached.Negotiations with Brussels have been led by the Treasury following the government's acquisition of a 43% stake in Lloyds and 70% of Royal Bank of Scotland last year.The pair want to transfer over half a trillion pounds of toxic loans to the state under the UK's asset protection scheme.Potential buyers of Halifax include supermarket chain Tesco. Chief executive of Tesco Personal Finance Benny Higgins used to run Halifax when he worked for HBOS.