The versatile 29-year-old had a switch to Camp Nou mooted the moment another managerial change was made in Catalunya. Having previously worked with Koeman in the Netherlands national team set-up, Wijnaldum emerged as an obvious option for Barca to explore.
He has entered the final 12 months of his contract at Anfield and Liverpool are eager to avoid losing any players as free agents. No extension talks have taken place on Merseyside for some time, though.
Barcelona are aware of that but are yet to formalise their interest by approaching Liverpool.
The Reds have no desire to sell at this stage and have been offered no indication by Wijnaldum that he is looking for a move. The uncertainty surrounding his contract is, however, keeping all options open.
Liverpool have several factors to take into consideration as they assess the situation. Wijnaldum’s age, along with his wage packet and role in Jurgen Klopp’s plans, will be considered.
He played more minutes for the Premier League champions in 2019-20 than any other midfielder at Anfield and was selected to be one of the Reds’ vice-captains behind skipper Jordan Henderson.
Koeman, however, was able to get the best out of him at international level and there is obvious appeal to be found in working with a familiar face at another of world football’s biggest clubs.
Any deal at this stage, though, would require Barca to free up funds from sales.
Were they to move players out in the current window and find themselves in a position to make a bid, then a suitable fee would have to be agreed with Liverpool.
The Reds would be reluctant to discuss such matters as things stand, but their situation could also change over the coming days and weeks.
Bayern Munich playmaker Thiago Alcantara continues to be heavily linked with a move to England, and his arrival could pave the way for departures.
When asked about the midfielder in his pre-match press conference, Klopp said: "That's an open contract situation, obviously, which means we don't talk about it.
"I never did in a press conference before, so why should I change it now. It's between the club and the player. It's all good in the moment, all fine. Gini looked good in pre-season and played a couple of good seasons for us. That's all I can say about that."