Bank of Ireland and AIB are vying for inclusion in the Dow Jones Eurostoxx 50, a key European index of blue-chip shares, when it is reviewed next month.
Both banking shares have surged in recent days, fuelled in part by the expectation that they might gain a coveted place on the index.
Such a listing boosts investor interest and demand for the shares.
Despite a weak performance by European banking stocks yesterday, AIB closed more than 3 per cent higher at €13.95, while Bank of Ireland gained 1.6 per cent to €12.60.
While theoretically the two banks could be included in the index, Davy analyst Mr Scott Rankin said it was unlikely both would get a place on it.
At last night's close, AIB, which has already held and lost a place on the index, was marginally ahead in the race for a listing. Using the Eurostoxx method of calculating market capitalisation, AIB was worth €12.2 billion, compared to Bank of Ireland's €11.9 billion.
"It's very close. It will be down to stock performance between now and the end of the month," one dealer said.
Which stocks are included in the revised index will be announced on September 2nd and the new index will become effective from September 23rd.
Inclusion is determined by a number of factors, including market capitalisation based on a company's share price at the end of August.
A place on the Eurostoxx index tends to boost demand for shares from the index-based and tracker investment funds that use it as a basis for their asset allocation.
Companies with a presence on the index are also more likely to appear on the radar screens of those institutions that operate on a pan-European, rather than a country-by-country, basis.
Bank of Ireland is currently ranked 49th among the shares that Stoxx, the Dow Jones company that operates the index, is considering for inclusion in the revised index.
AIB occupies 91st place on that list, which was compiled earlier this month using end-July share prices to determine the rankings. But AIB's strong rally over the last two weeks, which has seen it outperform its peers elsewhere, means that analysts believe it is now in the running for a place as well.
By contrast, although CRH occupies 59th place on the list, analysts don't expect it to make the top 50 next month because of its recent share price slide.
It will be the second time AIB has made an appearance on the index. Its previous inclusion in the Eurostoxx 50 in early 1999 proved a double-edged sword for the bank, however.
Initially, it triggered demand for the shares, helping to drive them to an all-time high of €18.20. But AIB shares lost around 40 per cent of their value some months later once it became clear that the bank was set to lose its Eurostoxx listing.
Iona Technologies is also feeling the downside of such listings at present.
The bruised technology stock lost around 17 per cent of its value in the US on Tuesday as funds sold the shares before it is dropped from the MSCI Ireland index, run by Morgan Stanley.
The sharp fall in Iona shares, which have plunged from more than $27 (€27.36) in January to less than $2, has knocked its market capitalisation, guaranteeing its elimination from the index, analysts said.
Iona shares did not trade in Dublin yesterday, closing unchanged at €2.45.
In New York, where they are mainly traded, there was no change and they finished at $1.77.