De Paul, 26, was tipped to leave Italy this summer with several approaches made.
He will continue at Udinese, but is conscious of interest from Atletico Madrid and welcomes it.
Speaking to Spanish daily Marca, De Paul was asked about Atleti’s interest in him.
“The reality is that I know Atletico Madrid were interested, with a coach like Cholo [Simeone], who caught my eye,” said De Paul.
“They play dynamic football that I like. Every training session seems like an official match for them.
“In Argentina, we grew up with that. Atletico is a very big club, a club that fights for important things. And if one day it happens, I would be very happy to go there.”
De Paul previously played in Spain for Valencia between 2014 and 2016, but was still a developing player.
Now in his fifth season with Udinese, De Paul is one of the most talented midfielders in Serie A.
He is also a regular in the Argentine national team and won 14 of his 17 caps in 2019.