Purists will argue Wijnaldum, an attacking midfielder, is the logical choice to inherit the iconic number 8 shirt - last worn by Reds legend Steven Gerrard - once his £25 million move goes through.
However, with the number 5 shirt also vacant, the Dutchman may wish to retain the one he already wears for Newcastle United.
The numbers 13, 29 and various others above 30 could also be available, but Talksport co-host Micky Quinn has claimed to have the inside scoop.
"He was offered the number 8 shirt and he wants the number 5 shirt," the Liverpudlian, who played for Wijnaldum's current employers, told the Alan Brazil Sports Breakfast show on Friday.
Traditionally a centre-half's number, Liverpool are not averse to handing out their 5 shirt - which hasn't been worn since Daniel Agger's departure in 2014 - to those who play in more unconventional roles.
Left-back Steve Staunton is a previous occupant, as is striker Milan Baros.
Gerrard wore the number 8 for 11 seasons, during which time he lifted the League Cup, FA Cup and Champions League.
Paul Stewart, Stan Collymore, Oyvind Leonhardsen and Emile Heskey are all previous occupants in the Premier League era.