Italian clubs wishing to participate in a breakaway Super League would be barred from playing in Serie A under new rules set to come into force this summer.
Three of the country's biggest clubs – Juventus, AC Milan and Inter Milan – were among the 12 sides who announced on April 18 they were forming a new competition.
The breakaway league collapsed within 72 hours after the six English sides withdrew.
The Sunday Times reported that the Prime Minister may have given Woodward – who has since confirmed he will step down from his position at the end of the year – the impression he would back the controversial move.
Asked about Johnson's talks with Woodward, the official spokesman said on Monday: "There was a very brief introduction to Ed Woodward, I think they crossed paths.
"But the European Super League was not discussed."
Pressed on whether Rosenfield told Woodward the Government would not oppose the new venture, the number 10 spokesman said: "No, that's not correct.
"The meeting was to discuss the safe return of fans and Covid certification as part of the events pilot work."
