The battle for bmi is not over yet, as Germany's Lufthansa confirmed on Monday it was shopping around for the best deal to sell the loss-making British airline, with Virgin Atlantic still in the running.

British Airways owner IAG said in November it had reached an agreement in principle to buy bmi as it seeks to squeeze more growth from its capacity-constrained Heathrow hub, but admitted that the deal was not exclusive.

We signed an agreement in principle with Virgin at the end of November, a Lufthansa spokeswoman said on Monday.

She added that Germany's biggest carrier hoped to sign a final deal in the next few weeks, with completion seen in the first quarter of 2012.

We will look at the quality of the offers and which one gives the most attractive prospects for the future of bmi, she said, declining to provide further details of the bids.

Lufthansa's shares were down 3.8 percent at 8.76 euros at 9:52 am, while IAG's fell 3.3 percent, underperforming the leading index of European shares <.FTEU3>, down 1.25 percent.

The Times newspaper in London earlier cited banking sources as saying the Virgin offer was thought to be in the region of 50 million pounds, while IAG's was about double that figure, excluding pension and restructuring costs.

Bmi comprises three underperforming businesses: a carrier serving Europe, the Middle East and Africa; bmi regional, serving the UK; and low-cost unit bmibaby.

Its key attraction is that it controls 9 percent of the coveted take-off and landing slots at London Heathrow, Europe's busiest airport, which is operating at full capacity after plans to build a third runway were scrapped

Virgin has maintained that a sale to IAG would lead to competition issues as British Airways is already the dominant airline at Heathrow.

British Airways' hold over Heathrow is already too dominant and we are very concerned, as the competition authorities should also be, that BA's purchase of bmi would be disastrous for consumer choice and competition, a spokeswoman said.

The Times said, without citing a source, that Virgin's bankers were arguing that Lufthansa would be better off doing a quick but lower-priced deal with the airline, as its offer would likely meet with less regulatory scrutiny.

Silvia Quandt analyst Stefan Kick said the Virgin bid was a good fall-back for Lufthansa, should competition authorities reject the IAG deal.

He added a sale to Virgin could also be a smart strategic move for Lufthansa as it would mean keeping bmi out of the hands of its strongest rival -- British Airways.

IAG said it was still negotiating. Lufthansa has kept us appraised of other parties involved in the process, an IAG spokeswoman said.

(Reporting by Stephen Mangan and Adveith Nair in London and Victoria Bryan in Frankfurt; Editing by Helen Massy-Beresford)