By Ben Hirschler

DAVOS, Switzerland (Reuters) - British Prime Minister Theresa May's Brexit plans are unlikely to lead to the re-establishment of a physical border or customs controls between Northern Ireland and the Irish Republic, Ireland's Finance Minister Michael Noonan told Reuters.

May said this week that Britain would not remain a full member of the European Union's customs union, potentially meaning a tighter border between the British province of Northern Ireland and the Irish Republic, which will be Britain's only land frontier with the EU once it leaves the bloc.

However, May has pledged to find a practical solution to preserving a common travel area between Britain and Ireland that predates their EU membership, while also limiting immigration.

Asked if this would make customs controls likely along a border that 30,000 people cross each day to go to work, Noonan told Reuters: "I don't think so and it's far too early to say."

"If you look at Mrs May's speech, she committed to the free travel area (between Ireland and the UK). She wasn't as strong on what she would like from the customs union; she said it might be associate membership," Noonan said in an interview on the sidelines of the World Economic Forum in Davos on Thursday.

"In other words, she opened up a negotiating space around the customs union and it is where that lands that will decide whether goods have to be checked on the border. But a lot of this can be done electronically now and it wouldn't necessarily mean a hard border."

Ireland's economy is widely considered at being most at risk from the departure of its key trading partner, but Noonan said trade data suggested there was no immediate impact and he expected an economic growth rate of "around 3.5 percent" to continue into the early 2020s.

In its most recent forecasts in October, Noonan's department said that gross domestic product (GDP) growth of 3.5 percent predicted for this year would slow to 2.8 percent by 2020 and 2.6 percent in 2021.

Noonan, who along with Prime Minister Enda Kenny is meeting senior executives in Davos to explore potential investment into Ireland, said Dublin had received around 100 "hard inquiries" from financial firms considering moving operations post-Brexit.

He said he was not concerned that President-elect Donald Trump could attack U.S. companies that continue to invest in Ireland and that there was no clear evidence of firms putting off investment while they await details of Trump's tax plans.

"There's a very strong pipeline of American investors coming into Ireland... now whether hidden in the statistics there are companies that are holding back slightly, I wouldn't know yet."

(Writing by Padraic Halpin in Dublin; Editing by Alexander Smith)