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Barca's sporting director Deco hasn't shied away from acclaiming Diaz, and his father has termed a potential move to the Camp Nou as a "dream."
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Meanwhile, Riyadh-based team Al-Nassr also appears to be monitoring the situation, envisaging Diaz as a potential marquee player, particularly if Cristiano Ronaldo departs.
"I feel I'm going through a really good period," he disclosed to the club's official site.
"I'm really happy to be here, to be part of this great institution, this great club and to have great team-mates around me.
"From the moment I arrived, I felt great pride.
I always tried to work hard for this, and to see that nowadays things are working out for me fills me with pride and I'm really happy because that's what I work for.
"[But] we are nobodies without our team-mates.
Diaz made a major contribution to Liverpool's triumphant Premier League title run.
Despite this, some high-profile sales may be necessary to balance the books.
Darwin Nunez, Harvey Elliott, Caoimhin Kelleher, and Andy Robertson are all names in the mix, but there's also chatter about the future of Diaz, whose market value could dip if he doesn't pen a new deal or depart soon.
"We will be talking, the talk about it (his future) will happen," Diaz revealed recently