People on both sides of those conversations have incentive to suggest it was a hefty sum: The Nationals have incentive to dispel any notion of their frugality with a legitimate offer. Team Boras has incentive to suggest Harper already has an unprecedented offer on the table, so as to generate even larger ones from other teams. Boras said he considered the offer represented a legitimate effort on the part of the Nationals, not the kind of just-for-show offer a team might make for appearances' sake.

Because Harper was under contract with Washington at the time, the team held exclusive negotiating rights with the former MVP. The Nationals tried to take advantage of that opportunity to strike a deal before Harper hit the open market. They have not yet made one.

Nationals General Manager Mike Rizzo addressed Harper’s situation Tuesday here at the general managers' meetings, saying only, “We took advantage of our exclusivity late in the season” to negotiate with Harper but “couldn’t reach a deal.”

That the sides did not agree does not rule out a reunion. Harper can explore pitches from other teams, well aware of what the Nationals have to offer, and decide from there. Boras always seems to circle back to the Nationals and other high-spending teams before finalizing any deals for major free agents, and he would almost certainly do so again with Harper, given Harper’s ties to Washington.

But that they did not agree likely means the Nationals will have to engage in the kind of bidding war they often try to avoid if they want to keep their superstar. Teams such as the St. Louis Cardinals, San Francisco Giants and Philadelphia Phillies have far more money to spare and fewer luxury tax concerns than Washington, which has now crossed that threshold two seasons in a row and is determined not to let the streak go to three.

That the Nationals made an offer establishes their interest in keeping Harper but does not necessarily clarify the extent of that desire. They could, if they wish, make an offer they know another team will beat, a move that would make them appear interested but not require actual commitment.

But people involved with the process indicated the front office held a genuine interest in consummating a deal with Harper. If Harper does not sign, the Nationals could still use an Opening Day outfield of Juan Soto, Victor Robles and Adam Eaton — a far cheaper option.

“I’m comfortable with the alternative [to Harper re-signing],” Rizzo said. “But I’m uncomfortable with the statement that we’re a better team without him.”

Rizzo admitted the Nationals will have to make their own decision on Harper at some point, even if Harper hasn’t made a decision on them. If he does not sign with them, they will allocate their financial resources elsewhere — and with plenty of holes to fill, they cannot afford to sit around and wait for the market to pass them by.

“It behooves us to have an expiration date,” Rizzo said, though he also indicated that he and his staff are negotiating with players on “parallel tracks” to cover all possibilities.

For years, those within the industry have speculated what it would take to lock down Harper, with no grand consensus other than he will likely command more than the 13-year, $325 million contract Giancarlo Stanton agreed to with the Miami Marlins in 2014. Harper has indicated that he would like that kind of long-term deal.

Barry Svrluga contributed to this report.