in a Portuguese publication Record claimed Ronaldo threatened to leave the World Cup after being told he would not start the last-16 win against Switzerland.
The Portuguese Football Federation (FPF) denied such an incident involving the 37-year-old and Santos explained the conversation the pair had.
“He has never told me that he wanted to leave our national team,” said Santos.
“It’s high time we stop with this conversation, stop the controversies.
“It’s high time for you to leave Ronaldo alone, in acknowledgement for what he’s done for Portuguese football.”
Santos, who was speaking before Saturday’s quarter-final against Morocco (15:00 GMT), also explained the conversation that took place when he told Portugal captain Ronaldo he would be dropping him against Switzerland.
“I spoke to him after lunch on the day of the game and invited him into my office,” said Santos.
“For obvious reasons Cristiano was not very happy about it as he has always been the starting player.
“He told me: ‘Do you really think it’s a good idea?’
“But we had a normal conversation in which I explained my viewpoints and of course he accepted them. We had a frank and normal conversation.”
Forward Ronaldo left Manchester United by mutual agreement before Portugal’s World Cup opener after a controversial interview in which the five-time Ballon d’Or winner heavily criticised the club.
He was substituted in both of Portugal’s opening games and Santos had said he “didn’t like” Ronaldo’s reaction when he was again replaced during the 2-1 group defeat by South Korea.
Goncalo Ramos started instead of Ronaldo against Switzerland and the 21-year-old scored a hat-trick in the 6-1 victory.
Ronaldo, who is Portugal’s most-capped player (195) and all-time leading goalscorer (118), was used as a late substitute in that game, but afterwards left the field while his team-mates were still celebrating victory