According to Sky Sports, the Netherlands international midfielder will speak to Klopp on Wednesday, with Spanish and European giants Barcelona interested in him.
The 29-year-old is keen on staying at the Premier League champions if an agreement can be reached on an extension to his current deal.
Wijnaldum joined Liverpool from Newcastle United in the summer of 2016 and is out of contract at the Reds at the end of the 2020-21 campaign.
The Dutchman has been a big success at Anfield, as he played an instrumental role in the Merseyside outfit winning the Champions League during the 2018-19 campaign and the Premier League last season.
Wijnaldum made 35 starts and two substitute appearances in the Premier League for Liverpool last season, scoring four goals in the process.