* U.S. dollar on track for best month since November

* Imminent U.S. rate rises still on investors’ minds

* European shares stay close to one-month high

LONDON, May 27 (Reuters) - The dollar rose on Friday while world stock markets were steady, as investors prepared for a likely hike in U.S. interest rates in the next few months.

The MSCI All-Country World equity index edged higher by 0.1 percent, with trading volumes relatively light ahead of public holidays that will close London and New York markets on Monday.

The pan-European FTSEurofirst 300 index of leading European shares was steady but remained around a one-month high reached earlier this week, while U.S. futures made slight gains.

“Markets are doing remarkably well given that a U.S. interest rate rise might happen as early as next month,” said Lex Van Dam, hedge fund manager at Hampstead Capital.

The dollar index rose 0.1 percent and was on track for its best monthly performance since last November, after a string of U.S Federal Reserve officials indicated that rates could rise as soon as June given signs of strength in the world’s biggest economy.

Investors will looking for further clues on the likely timing of a rate hike when Federal Reserve Chair Janet Yellen speaks later in the day.

“I’m not sure if U.S. interest rates will go up in June, but July is quite likely,” said Clairinvest fund manager Ion-Marc Valahu, who added that he had recently cancelled some earlier “short” positions that bet on the dollar losing ground.

A stronger dollar often lifts European stocks as weakness in the euro makes European companies’ exports cheaper.

Some traders said stock markets were unlikely to make much headway in the coming month, however, given uncertainties like Britain’s June 23 vote on its membership of the European Union.

“With the headwinds of a possible interest rate hike from the Federal Reserve, and the EU referendum in June, there might not be a huge amount of new money coming into the market,” said Manoj Ladwa, head of trading at TJM Partners. (Additional reporting by Anirban Nag and Alistair Smout in London, and Shinichi Saoshiro in Tokyo; Editing by Catherine Evans)