TOMORROW the gloves come off in what could be the final fight for control of the London Stock Exchange.

Nasdaq, the US high-tech stock exchange, will be free to bid for the LSE as the six-month freeze imposed after its swoop to mop up 25% of the exchange’s shares earlier this year falls away.

If Bob Greifeld, Nasdaq’s chief executive, does charge in with a bid he must offer the £12.43 paid for the two blocks of shares bought earlier this year. But if Greifeld waits for another six months, he is free to come back and offer whatever price he believes is appropriate.

Exchange watchers are as divided as ever over what they expect Nasdaq’s tenacious boss to do. But most believe that Greifeld is more than ready to bid immediately at £13 — although not until later this month — because it is the Jewish Yom Kippur holiday this week. He has the financing in place and believes the commercial arguments are on his side.

Others are convinced Greifeld will wait at least a few weeks to watch what happens to the LSE share price, letting the hedge funds, which hold some 30% of the shares, sweat a bit more, before storming in with a hostile bid.

“He’s in this for the long game,” said one analyst. “More important, he’s the only man who has actually put money on the table — £640m — and has built a commanding position in the consolidation game.”

Not all agree. Another analyst said Nasdaq couldn’t afford to wait, but would have to move quickly because the LSE share price was relatively cheap at the moment considering the stunning growth experienced by the London market.

“Analysts are putting a floor of £12 on the LSE as a stand-alone operation and without any bid premium. If you take that view, then it follows that a bid at £13 looks cheap and a steal for Nasdaq,” he said.

At the LSE’s Paternoster Square offices, chief executive Clara Furse is on bid alert again. She has already repelled four bid approaches in two years — from the Deutsche Börse, Euronext, the Australian financiers at Macquarie, and now Nasdaq.

So far Furse has been able to fight them all off, but Nasdaq is a quite different aggressor, and she knows it.

That’s why Furse held detailed talks with Icap, the world’s biggest inter-dealer broker, about a £6 billion merger to create what would be one of the world’s biggest electronic trading platforms.

Icap and the LSE held serious discussions over the summer, but these were called off a few weeks ago because Icap felt a merger would be dilutive to its shareholders.

However, sources close to both sides say there is still a strong desire to do a deal if the right price and terms can be agreed to justify the price being paid. If Nasdaq were to bid, the situation could change swiftly.

Furse and Icap chief executive Michael Spencer believe there is a compelling logic to creating a London-based British powerhouse by merging their two businesses.

They started talking about an agreed, friendly merger early in June after the LSE’s advisers, Merrill Lynch, approached the Icap boss.

But Spencer, who owns 20% of Icap and is one of the City’s richest men, worth £600m, is said to be cautious about over-paying for the exchange.

“He’s not yet confident about the LSE’s longer-term growth to justify the current price or any bid premium,” said one insider.

Furse been criticised for not being pro-active enough in the consolidation game now being played between exchanges. But she has been extremely effective in building the LSE’s core business and turning London into an international magnet to attract overseas companies.

So far this year, for example, three times as many companies listed on the LSE as on Nasdaq and the NYSE combined, while its Stock Exchange Trading System (Sets) trading volumes continue to grow at more than 20% a year because of the huge leap in algorithmic trading. Results in November are likely to show record profits again.

Nasdaq’s Greifeld feels that a deal with the LSE would be good for shareholders and also for market issuers and traders.

Nasdaq’s advisers, which include Greenhill and DrKW, believe that between $60m (£32.1m) and $100m of costs can be taken out of the merged group by using its electronic trading system Inet rather than the LSE’s Sets. It estimates that trading costs could be brought down to US levels.

Nasdaq, which is the smaller of the potential partners at £1.8 billion, compared with the LSE’s current £2.6 billion price tag, has financing in place to underpin any share or cash offer it may be considering.

Greifeld also believes that if Nasdaq does bid, there will be no major regulatory or political problems.

Recent referrals to the competition authorities of the putative bids by Euronext and Deutsche Börse for the London Stock Exchange centred on clearing, but Nasdaq is a pure trading system.

Others are not so sure. The Competition Commission has looked at previous bids and could find reasons of public interest to thwart a bid.

Nasdaq also finds no problems with the recent intervention of Ed Balls, the Treasury’s minister for the City, who promised legislation to prevent any foreign buyer from changing the LSE’s regulatory regime in the event of takeover.

Furse’s fight is being made all the more difficult by the hedge funds, which now hold at least 30% of the LSE shares on the register. Most of the hedge funds bought at about £11.52 a share upwards and will want some premium before they sell out. In recent weeks stock lending in LSE shares has increased again, as the funds continue to put pressure on the exchange.

Greifeld is said to think that LSE’s options are running out.

The only serious alternative bidder is Icap’s Spencer, another seriously determined man. Up to now, Spencer has carried out all his big deals — the bids for BrokerTec and EBS, the foreign-exchange platform — behind the scenes and by agreement.

Will this be the deal that brings him out for a bare- knuckled spat to take the lead in the world’s exchanges?