Hall of Fame columnist Peter Gammons reported the news Friday on 670 The Score.
He said the "people" told him that Harper would "prefer to play for the Cubs."
The Nationals signed Harper to a one-year, $21.6 million contract in May, avoiding arbitration.
Massaging Harper's high asking price onto is payroll might be a difficult task for the Cubs. Gammons added that he doesn't "think it's going to ever happen."
Cubs third baseman Kris Bryant is making $1.05 million this season and is arbitration eligible from 2018 through 2021. He is also expected to seek a lucrative deal. Scott Boras represents Harper and Bryant, the last two MVPs of the National League. The Cubs also handed Jason Heyward an eight-year, $184 million contract during the 2016 offseason.
In December, a high-ranking Nationals executive told USA Today that Harper will demand a deal longer than 10 years and exceeding $400 million.
Harper, 24, is hitting .328 this season with 15 home runs and 43 RBI. He is currently serving a three-game suspension for his role in an altercation Monday with San Francisco Giants pitcher Hunter Strickland. He is eligible to return Sunday in the Nationals' 4:05 p.m. matchup against the Oakland Athletics at O.co Coliseum.