The Czech attacking midfielder, who joined Lyon from Viktoria Plzeň, ultimately remained in France after the two clubs failed to reach an agreement.
“When Juventus contacted me I was a little stunned. A big club, a fantastic history, a beautiful stadium, Italy and a strong Czech presence... It was exactly what I and my partner Natali liked.”
Šulc said he would have been open to the move if Juventus and Lyon had agreed terms.
“If the two clubs had agreed, I certainly wouldn't have objected. But the offer wasn't interesting enough and so everything fell through.”
Corentin Tolisso also played a role in Šulc's decision to remain at Lyon, encouraging the Czech midfielder to stay during a period of uncertainty.
“If you leave I'll understand, but I really hope you stay,” Tolisso reportedly told him.
Šulc arrived at Lyon for around €7.5 million and scored 11 goals while providing three assists in 27 Ligue 1 appearances last season.
His first five appearances of the new campaign have already produced three assists, underlining his importance to Paulo Fonseca's side.
The summer was more complicated for Šulc, however, with a knee problem followed by a disappointing World Cup campaign for the Czech Republic, who finished bottom of their group with one point.