"We have good reason to believe that a nomination we received concerning Trump has been falsified," Nobel Institute director Olav Njolstad told AFP.
He refused to provide further details, saying it was for the police to give more information.
Each year, nominations for the Nobel Peace Prize must be submitted by January 31. Among those entitled to propose names are members of parliament and government, former laureates and some university professors.
While the list of candidates is kept secret for at least 50 years, those who nominate are however allowed to disclose their choice.
The Peace Research Institute of Oslo (Prio) said in early February that Trump's name was on the list.
It is possible that this nomination was submitted by a person suspected of committing identity fraud to appear eligible to nominate.
The Nobel Institute said it had received 329 valid nominations for the 2018 Peace Prize. The five members of the Nobel committee that selects the winner are also allowed to submit names during their first meeting of the year, which was held on Monday.
The name of the 2018 winner will be announced in early October
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