The Nationals can simply not afford to have Fielder, Strasburg, Harper, and Zimmerman at the same time. They certainly can not afford him after signing Jayson Werth to a lucrative deal last season and with the most recent acquisition of Gio Gonzalez from the Oakland A's. There is just not enough money to go around.
Another thing to consider: Scott Boras, Fielders agent, is known for giving his players high priced deals (see: Jayson Werth). Boras is also the agent for Stephen Strasburg, Bryce Harper, and Danny Espinosa. While the Nationals and Boras have a history, Boras has a history of getting the most money for his clients. Just because the Nationals have the money to spend does not mean that they have to spend it.
Is it even practical to sign Fielder to a lucrative contract? Let's look at the Nationals other first baseman.
The Nationals currently have Adam LaRoche, Michael Morse, and Chris Marrero at the first base position. Just last season the Nationals went out and signed LaRoche. He ended up getting injured and Michael Morse played a majority of the season at first base. LaRoche and Morse are both threats at the plate and in the field. The Nationals could better serve themselves by spending that money elsewhere.
The rumor of the Nationals being the frontrunner's to sign Fielder is no more than speculation and a rumor. The Nationals front office has been adamant that Adam LaRoche is going to be the teams first baseman this year and they have not yet commented on this rumor.