Liverpool are holding further talks with Paris Saint-Germain on Tuesday for Bradley Barcola.
There has been a gap in valuation between the two clubs throughout the summer, with PSG asking for around £145m for the France international.
However, the discussions that have taken place during this window have been described as positive, and there is optimism that a deal can be struck with a week left before the deadline.
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Sky Sports News understands there are good relations between the two clubs at the highest level. It is hoped this will help Liverpool and PSG reach an agreement.
Liverpool have also explored a move for Barcola's team-mate, Ibrahim Mbaye, who plays off the right wing.
The Premier League club's priority throughout this window has been to reinforce in wide areas.
They have been pursuing Barcola and Mbaye, while Brighton have also rejected two Liverpool offers for Yankuba Minteh, the latest being £60m.
Liverpool are currently the only club chasing Barcola, who has entered the final two years of his deal and has grown dissatisfied with his role at the European champions.
Liverpool, meanwhile, do not want to sell Cody Gakpo amid interest from Tottenham and Manchester City and would likely need two new wingers in before considering letting the Netherlands international go.
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