Nigerian President Muhammadu Buhari is to meet King Salman before travelling on to Qatar.
The official Saudi Press Agency reported late Monday that Buhari had landed in Riyadh, where the governor, Prince Faisal bin Abdulaziz, welcomed him.
It gave no details of the expected discussions.
Buhari arrived the week after Saudi Arabia and Russia agreed in Doha to stick to January production levels if others followed.
The potential output freeze aims to stabilise a market in which prices have fallen to their lowest levels in nearly 13 years.
Poorer OPEC members, including Nigeria, have been hard-hit by the price drop but even the wealthy Gulf states have been forced to adopt austerity measures to cope with falling oil revenues.
"Nigeria of course is likely to support such a freeze. So I wouldn't be surprised to see them voice their support to the freeze agreed in Doha," Abhishek Deshpande, lead oil market analyst at Natixis in London, told AFP.
But he added that unless Iraq and Iran also commit to limit production such talks "carry very little weight."
The two countries are OPEC's second and third largest producers.
Prices have plunged since 2014 when the Saudi-influenced OPEC refused to cut production in an increasingly competitive market, particularly from American shale oil producers.
Russia, which produces about 10.7 million barrels of oil a day, does not belong to the Organization of the Petroleum Exporting Countries (OPEC), in which Saudi Arabia is lead producer and Nigeria a smaller member.
Iran, which is returning to world markets as sanctions are lifted under a nuclear deal, said it supported the Saudi-Russia move, but stopped short of committing itself to any production curbs.
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Saxo Bank analyst Christopher Dembik told AFP that, on the one hand, Nigeria supports the mooted freeze but at the same time wants to increase its production to respond to domestic market needs.
Nigeria could be 'crucial'
This could be addressed during Buhari's Saudi visit, Dembik said.
"In the longer term, there is no reason why the country won't align itself with the position of Saudi Arabia and Russia," Dembik said.
Nigeria and Saudi Arabia will also discuss their position towards Iran and Iraq, he added.
"Nigeria could have a crucial role in this respect because of its measured position" that Iran and Iraq should elevate their production before envisaging a freeze on their part, Dembik said.
"It is probable, then, that Nigeria meanwhile establishes a bridge for negotiations, notably between Riyadh and Tehran."
According to OPEC's Monthly Oil Market Report, Iraq produces about 4.4 million barrels a day, followed by Iran at more than 2.9 million.
Saudi Arabia's output is close to 10.1 million barrels a day, according to January data.
Buhari is accompanied by Emmanuel Ibe Kachikwu, the junior oil minister and head of the state-run oil firm, the president's office said in a statement.
Efforts by Nigeria and other OPEC members to achieve greater price stability "are expected to be high on the agenda of discussions between President Buhari and the Saudi monarch," the statement said.
Oil prices dipped in Asia on Tuesday as traders remained doubtful that talks on an output freeze would lead to agreement.
US benchmark West Texas Intermediate crude for delivery in April, a new contract, was down 73 cents, or 2.19 percent, at $32.66. Brent for April dropped 67 cents, or 1.93 percent, to $34.02 a barrel.
Prices have plunged from above $100 a barrel in early 2014.