In the aftermath of Tuesday's comprehensive 4-0 victory over Everton in the 222nd Merseyside derby at Anfield, the Reds boss said he was confident he still had time to bring someone in.
He said he was targeting a major signing and Dnipro Dnipropetrovsk's Ukraine international Konoplyanka, valued at around £16million, would fit into that bracket.
The player's father Oleg increased speculation about a move to Anfield by telling Ukrainian media outlet Tribuna: "I do not want to say specifically but the information about a transfer to the English club is true.
"He can change clubs later this week. We do not consider offers from Ukraine."
Having missed out on long-term target Mohamed Salah after the Egypt international instead opted for Chelsea, Rodgers is keen to make an addition before Friday's deadline.
There has been growing discontent among fans that no progress was being made to strengthen a squad which is severely depleted by injuries despite being in a battle to secure a top-four finish.
"I think we will hopefully do something over the next couple of days," said Rodgers.
"Hopefully we can have a major signing before the window shuts and if we can do that we will be set up for the remaining games."
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Source: PA