Bradley Barcola is keen to remain at Paris Saint-Germain after sources told ESPN the European champions rejected two approaches from Liverpool for the 22-year-old.
Sources have told ESPN that PSG, who are not open to a transfer, rejected one approach from Liverpool earlier this summer and a second on Wednesday.
Bayern Munich have also made an approach which has been turned down.
The Premier League champions are looking for another forward after Luis Díaz's move to Bayern Munich and Darwin Núñez's likely exit to the Saudi Pro League.
Liverpool have made one offer for Newcastle United's Alexander Isak, but a source has told ESPN that the club are not currently planning a second bid for the striker.
The Merseyside club have long admired Barcola, who has also played as a false nine under PSG head coach Luis Enrique at the Parc des Princes. The France international arrived in Paris from Lyon in 2023.
- Full men's Ballon d'Or list: Yamal, Dembélé headline list
- Isak excluded at Newcastle, told to train alone - report
- Liverpool transfers: Al Hilal agree Darwin Núñez fee - sources
Barcola is rated as one of the most talented young players in Europe, but he is battling with Ballon d'Or favourite Ousmane Dembélé and PSG's breakout star Désiré Doué for a place in Enrique's starting XI.
He has scored 26 goals and registered 30 assists for PSG in all competitions.
Information from ESPN's Beth Lindop contributed to this report.