Netanyahu made the comment late Saturday before boarding a flight to the United States.
"I'll definitely discuss with him that possibility," Netanyahu said in response to a journalist's question on whether he planned to invite Trump for the occasion.
"I'm very grateful to him for this historic decision to recognise Jerusalem as Israel's capital and to move the American embassy to Jerusalem on our independence day," he said.
The May 14 date of the embassy opening coincides with the 70th anniversary of the founding of Israel.
For Palestinians, the date represents the anniversary of the Nakba, or "catastrophe", in which hundreds of thousands either fled or were expelled from their homes in the war surrounding Israel's creation.
Trump's December 6 Jerusalem declaration outraged Palestinians and broke with decades of international consensus that the disputed city's status must be negotiated between the two sides.
Other countries have their embassies in Tel Aviv.
The new embassy will initially be located in a US consular building in Jerusalem while Washington searches for a permanent location.
Israel occupied mainly Palestinian east Jerusalem in the 1967 Six-Day War and later annexed it in a move never recognised by the international community. It sees the entire city as its capital.
The Palestinians see east Jerusalem as the capital of their future state.
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