The 22-year-old midfielder is currently starring for Spain at the European U21 Championship.
He is one of the more experienced performers at that competition, having made close to 150 appearances for Atletico – including plenty of Champions League outings.
Considered to be one of the most promising players in European football, the admiring glances being shot in his direction come as no surprise.
Saul has sought to play down the rumours suggesting a summer move could be on the cards, but did tell reporters while away in Poland: “I am happy at Atletico and I feel valued but everyone would like to earn a bit more money to be able to help out the family.
“I’m fine at Atletico. I don’t want to leave. It was hard to get the confidence of Cholo [Diego Simeone] and now that I have it, it would be very difficult to start from zero at another team.
“I don’t see myself outside Atletico, something very surprising would have to happen.”
Saul is clearly not looking for a move elsewhere, but he has not completely closed the transfer door either.
Barca are reported to see him as a possible alternative to long-term target Marco Verratti of Paris Saint-Germain.
Any interested party would, however, have to meet a €80 million release clause.