Lookman was born in England but can play for Nigeria through his parents.
"He has Nigerian parents and we'd need to speak to him first," Nigeria Football Federation (NFF) official Bitrus Bewarang told BBC Sport.
He made a goalscoring debut in the side's 4-0 win over Manchester City on Sunday and has caught the attention of Bewarang
"I saw him against Manchester City and I was excited to see a young player of Nigerian descent shine, so I thought why not," said Bewarang.
"It is the duty of the national coach [Gernot Rogr] to invite players to the national team, but we will help him check Lookman's eligibility."
"We've managed to get players like Moses and Iwobi in the past and Lookman will be a great addition to the national team if we got him," Bewarang added.
"I am not desperate to see this happen but we will give it a shot."