New boss Ronald Koeman has made it clear to the Spanish giants' hierarchy he is keen to bring his fellow Dutchman to the Nou Camp.
Wijnaldum, 29, is into the final year of his contract and could leave Anfield next summer for nothing.
But Barca are believed to want him this year and, although they have yet to make contact with the Reds, are considering an offer.
Koeman has spoken of Wijnaldum's quality and said: “First of all, he plays for a great team at a high level. He is also more experienced that he was a couple of years ago.
“He is a so-called multi-functional midfielder. His best position is to play as an attacking midfielder, but at Liverpool he’s shown he’s able to play as a controlling midfielder.
“He’s a team player as well. He’s not someone who thinks he is more important than the team.
“He always tries to make other players better. He is a great player to work with.
Get the latest transfer news straight into your inbox!
Want to be on the ball with all of the latest football news?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
“He’s had a difficult time in the Dutch national team — now he is ready to reach his level at Liverpool.”
Liverpool would look to replace Wijnaldum if he leaves this summer which would open the door for a move for Bayern Munich midfielder Thiago Alcantara.
The Reds have been heavily linked with the Spain ace this summer, who also has just one year left on his contract.