Wijnaldum’s current deal with Liverpool is due to expire next year.
But Koeman, who managed the midfielder with the Dutch national team, wants to make the 29-year-old his first signing at the Nou Camp, according to Algemeen Dagblad.
DAILY POST recalls that Koeman, 57, was confirmed as Barcelona head coach on Wednesday.
The Dutchman took over from Quique Setién, who was sacked on Monday after their Champions League’s exit in the hands of Bayern Munich last week.
Speaking to Barcelona’s official website after signing a two-year contract as Blaugrana boss, Koeman admitted that he would have to “work hard to strengthen the team” and Wijnaldum could be one of those new additions.