Press Association Sport understands the Reds will pay a maximum of £25million for the Holland international, taking into account various add-ons.
It is believed Wijnaldum’s former club PSV Eindhoven are due a sell-on fee for a player who moved to St James’ Park a year ago for £14.5million.
Manager Jurgen Klopp has been looking to strengthen his midfield options and turned his attention to Wijnaldum after giving up their pursuit of Udinese’s Piotr Zielinski.
With the arrival of the attacking midfielder imminent it makes it more likely Joe Allen will depart.
The club accepted a £13million bid from Stoke for the Wales international, who has less than a year left on his contract, but Swansea and Celtic, managed by former Reds boss Brendan Rodgers who brought Allen to Anfield four years ago, are also interested.
Burnley have also proposed a season-long loan deal for defender Jon Flanagan, who did not play in Wednesday night’s friendly win at Huddersfield or travel with the squad to the United States just a few hours later for the second leg of their pre-season preparations.
Klopp will have most of his squad in America as those not involved in the latter stages of Euro 2016 have joined the tour party, such as those who played for England and Belgium.
“It is a real challenge for us because we bring the two groups together,” said the Reds boss.
“Some (the ones who have featured mostly in the four domestic friendlies) have been training for five weeks because they had to start two weeks before they started with us and these players (joining the group) have had two weeks off and only one week training.
“We have to bring the fitness levels together.
“At this moment I have no idea who I will play in our first friendly game in the US, I think we have 15 or 16 players who could go 90 minutes and we will see how the English and Belgian boys are.
“We have worked with different groups. The good thing with a training camp is you have nothing else to do so we can be fully concentrated on the things we have to do.”
Midfielder Lucas Leiva, who sustained a hamstring problem which forced him off in the second half against Huddersfield, did travel with the squad and will be fully assessed once the team are settled in their California training base.
Wijnaldum will join his new team-mates in the United States once his move is concluded over the weekend.