Not likely. Buster Olney of ESPN talked to a group of executives and the prevailing opinion was that Harper will re-sign with the Nationals. Joel Sherman of MLB Network and the New York Post found the same thing when he talked to executives. FWIW, Jack Curry of YES agrees with them.
The salaries for Corbin and Gomes essentially replace those of Wieters, Gio Gonzalez, and Madson. They still have Murphy’s money and others off the books, and the luxury tax threshold is going up from $197 million to $206 million.
If the Nationals didn’t win with Harper and Soto, how do they win with Soto and NOT Harper?
https://www.mlb.com/news/nationals-still-interested-in-bryce-harper/c-301465556
Harper tends not to be an impact player. He performs poorly when it really matters. He is also selfish and aloof and doesn't contribute much to the clubhouse. I don't think the Nats really need him, especially at the number he will be asking.