(Updates Friday story with developments in Mexico election in paragraph 12, outcome of OPEC+ meeting in paragraph 17)

May 31 (Reuters) - The start of a new month can mean only one thing for investors: time for the all-important monthly U.S. employment report, but also for a likely European Central Bank rate cut, as well as the outcome of India's marathon general election.

Here is a look at what's happening in markets in the coming week, from Ira Iosebashvili in New York, Swati Bhat in Mumbai, Yoruk Bahceli in Amsterdam, Anousha Sakoui and Amanda Cooper in London.

1/COOL STORY

Is the U.S. economy finally cooling? It will take several months of data to answer that question, but one key piece of the puzzle comes with the closely watched employment report, out on June 7.

Investors had been worried that an overly strong economy might prevent the U.S. Federal Reserve from lowering rates this year at all, or even require a rate rise. But those concerns were put to rest last month, albeit temporarily, by data showing slowing inflation and a cooling labour market.

Still, policymakers have urged patience on rate cuts, saying they would like to see several months of data to be sure inflation is heading back towards their 2% target. The employment report could prove the economy is losing steam if it shows the slowdown in job creation has continued.

2/BIG ELECTIONS, BIG CONSEQUENCES

India's six-week long national election is in its final stages, with votes due to be counted on June 4. Investors are gearing up for Prime Minister Narendra Modi securing a third term in office.

Markets see a Modi win as providing political stability and continuity in India to support sustained economic growth.

Indian equities outperformed most major markets in 2023 and are already trading at lofty valuations. They could get another boost if Modi remains in power, even as part of a coalition government.

Mexicans also went the polls on Sunday, at which ruling party hopeful Claudia Sheinbaum looks set to win a landslide victory to become the first woman president. The peso has sold heavily in the past week, as traders ponder the uncertainty for the economy stemming from the vote.

3/IT'S A GAS, GAS, GAS

The oil market is entering into a sweet spot in the year - the summer driving season in the United States. The price of crude is up 10% year-on-year and intensifying Middle East tensions are keeping the market nervous.

Meanwhile, gasoline futures have fallen by 7%, offering a potential boon to customers at the pump. But, U.S. gasoline inventories aren't declining as quickly as they ordinarily would at this time of year, which suggests consumption isn't quite hot enough to put a dent into supply. A measure of demand for immediate delivery of crude is also around its lowest since December .

A lot is riding on the outlook for growth and, therefore, demand for fuel. The world's biggest oil exporters agreed on Sunday to extend most of their deep oil output cuts well into 2025, as the group seeks to shore up the market in the face of tepid demand growth.

4/UK FOR SALE

BHP Group may have failed in its bid for Anglo American, taking $49 billion out of bankers' league tables. But the emergence of the bid in April highlights a revival in UK M&A.

April saw 38 companies in the UK under offer, the most since June 2022, according to Peel Hunt. Take one away and that high-water mark doesn't change.

Bankers pinpoint that it's companies driving the charge, and they expect more UK deals, as the interest rate outlook and economic backdrop stabilise and competition from private equity funds for assets is still muted.

Driving the inbound interest is the persistent cheapness of UK assets. The FTSE 100 12-month forward price-to-earnings ratio continues to trade at the widest discount to the S&P 500's since at least 1990, and lags the performance in the pan-European STOXX 600 and Germany's DAX.

5/CUT IT OUT

The ECB is all but certain to become the first major central bank to cut interest rates this cycle on Thursday.

Policymakers have practically promised a June cut that is expected to lower the bank's key rate by 25 basis points to 3.75%. So all focus will be on what hints ECB boss Christine Lagarde gives on what happens next.

Inflation in the bloc's dominant services sector remains sticky and its economy is recovering faster than expected, while a closely-watched wage growth figure accelerated last quarter, leaving the outlook beyond June less certain.

Traders are still much more confident that the ECB will cut rates multiple times this year compared to its U.S. and British peers, though they have also reduced their bets on its moves.

They now expect two cuts and less than a 50% chance of a third - compared with three when the ECB last met and at least five at the start of the year.

(Compiled by Amanda Cooper; Graphics by Prinz Matgulis, Editing by David Holmes and Sonia Cheema)