Barcelona will be desperate to put the Messi transfer drama behind them quickly with the start of the season just over a week away.
Koeman has also made it clear that he wants to build his own squad at Barcelona and Wijnaldum would come in as a proven champion.
The 29-year-old was the most used midfielder at Liverpool last season as they won the Premier League title while he also broke Barcelona hearts in 2019 on their way to Champions League glory.
Liverpool are unlikely to sell unless their valuation is met, but Barcelona may well push forward with a deal to start trying to win Messi over – and the Reds’ links to ex-Barca midfielder Thiago Alcantara of Bayern Munich and their need to sell players to fund moves means a move may make sense for all parties.