On Monday, Trump said during a meeting with congressional leaders in the White House that "3 to 5 million illegals" voted, according to two Democratic aides who spoke on condition of anonymity.
Spicer told reporters Tuesday "maybe we will" launch an investigation into Trump's claims.
"Anything's possible, I think, at some point," he added. "There is no investigation. I said it was possible. Anything is possible. It was a hypothetical question."
Trump has made repeated claims about voter fraud after losing the popular vote in the election in November, though thus far, no evidence has been presented that backs up his allegations.
"He continues to maintain that belief based on studies and evidence people have presented to him," Spicer said Tuesday.
At least five reporters asked questions on the issue during the press briefing, and at one point Spicer dismissed the suggestion that Trump kept bringing up the topic of the unsubstantiated voter fraud because the president was upset about the vote count. Spicer said Trump "won very handily" and "he's very comfortable with his win."
When pressed for specific evidence supporting Trump's "long-standing belief," Spicer cited a 2008 study by Pew Research and "other studies that have been presented to [Trump]."
The Trump transition team was previously asked about this topic and cited the Pew study, which came out in 2012 and focused on the results of the 2008 election and the need to update voter registration rolls.
The primary author of the study in question previously responded, tweeting that "the report made no findings re: voter fraud."
Spicer did not give names or sources for the other studies.
"We'll see where we go from here, but right now the focus that the president has is putting Americans back to work," Spicer said.