However, the club passed up the opportunity because they feared that Ronaldo’s £1 million per year salary would upset the dressing room.
Thompson told The Athletic: “He was being touted around everyone.
“Tony Henry, the former Man City midfielder, was working for (agent) Paul Stretford, who was tasked by Jorge Mendes to drum up interest in England.
“They were desperate to get Ronaldo out of Sporting and invited me over for a game. I was told the fee was £4 million but they explained that it could be paid over the course of a four-year contract so essentially it was £1 million per year.
“I asked what kind of salary he would want and they said it was £1 million per year after tax. That was a lot for an 18-year-old kid but they said that was negotiable.
“It was a Sunday and I explained to them that I needed to go back to Liverpool and speak to Gerard Houllier and see what we could do. I fed all the information back to Gerard, who said he would speak to [chief executive] Rick Parry.
“Lo and behold, the following week I’m at Melwood when the yellow ticker on Sky Sports News says, ‘Manchester United sign Cristiano Ronaldo from Sporting for £12.2 million.’ I couldn’t believe my eyes.
“How had the fee gone up from £4 million to £12.2 million in a few days? Gerard asked me to phone Tony to find out what had gone on. Tony told me that when he’d got off the plane on the Monday he had got a call to say he was off the deal. It was down to Stretford and Mendes instead.
“It was astonishing that the fee trebled. He was clearly a big talent but no one could have predicted back then how great he was going to be.”
Arsenal nearly signed the Portuguese sensation as well, but Manchester United showed more urgency and were willing to offer more money.
“The obvious player [Arsenal missed out on] that comes to mind is Ronaldo. He was here with his mother and we were very close,” the former Gunner boss told Arsenal.com.
“Then Man United came in and they had Carlos Queiroz at the time, who was their coach. United played against Sporting Lisbon and Ronaldo was outstanding and they signed him.
“There is always something you could have done differently but the problem of negotiations is to know when you give in and when you don’t give in. Once we were at £4.5m, we were still in negotiations. David [Dein] met with [the agent Jorge] Mendes in Paris and he was representing Sporting, so we were very close but Man United went to £12m, which we could not afford.”