A trial is currently underway in Costa Rica's capital, San Jose, with players Navas, Bryan Ruiz and Celso Borges having sued former federation executives, Adrian Gutierrez and Juan Carlos Roman for defamation.
Gutierrez claimed in a 2018 radio interview that during a meeting four years earlier those players had threatened to lose games on purpose if the federation did not part ways with then coach Jorge Luis Pinto.
However, Gutierrez was not present in that meeting in which Navas, Ruiz and Borges attended as team captains.
The current federation president, Rodolfo Villalobos, was also at the meeting, as was the federation treasurer. Li, who presided the Costa Rica Federation in 2014 and was banned for life by FIFA in 2017 in bribery case, testified on Monday as a witness of the defence.
He said that after telling the players at the meeting that the FA's intention was to renew Pinto's contract, it was then when Navas mentioned a clause in the contract of the national team coach in which if he lost three consecutive games there was cause to terminate his contract.
Li also stated that Ruiz had told him that he was prepared to quit the national team if Pinto continued in charge.
Navas, the starting goalkeeper of Paris Saint-Germain, and Ruiz, testified on Friday denying they had threatened to lose games intentionally and that the comments made by the defendants had affected their dignity and image.
"It is not something that has come out of our mouths and it will never happen, because we have been professional footballers for many years, we have an honour and a prestige to defend," he told the newspaper Extra.
Ruiz did confirm that he had said in the meeting that he would walk away from the national team if Pinto continued due to alleged disrespectful treatment by the coach towards the players.
Under Pinto's second spell in charge of Costa Rica, the national team had their best ever World Cup performance when they went unbeaten to the quarterfinals of the 2014 tournament in Brazil before losing to the Netherlands on penalties.
Pinto, whose contract was not renewed, took over the Honduras national team in December 2014.
The Colombian tactician testified on Tuesday via video link and said: "President Li and I had a meeting and I remember perfectly he took me to one side and said 'the players say that if you continue they will lose two or three games so as to get you out.'
"I told them 'let's not get into that problem, you [federation] and your country are going to be affected.' I had offers and told them that I said that I would like to speak to all the players and ask them that," Pinto said.