Liverpool and Tottenham are understood to be fighting it out to sign Dnipro Dnipropetrovsk winger Yevhen Konoplyanka before the transfer deadline.
Liverpool managing director Ian Ayre flew out to Ukraine this week to discuss the signing of the 24-year-old, who has made 35 appearances for his country.
However, it has now emerged that the Reds face stiff competition from Tottenham for his signature.
Liverpool have yet to recruit anyone this month and missed out on Egyptian winger Mohamed Salah, who left Basel for Chelsea despite holding talks about a move to Anfield.
Following his side's 4-0 victory over Everton in the Premier League on Tuesday, manager Brendan Rodgers said that he was hopeful of making "a major signing".
"I think we will hopefully do something over the next couple of days," he said.
Rodgers' plans could still be scuppered again, though, if Tottenham manage to agree a deal with Konoplyanka before the window closes on Friday evening.