"This is always a crucial period. The league table always looks so much different at the beginning to mid-January than what he does at the start of December," Milner was quoted as saying by British media.
"You see suspensions and injuries taking hold and teams losing and gaining form. It is a great time to be in good form going into this Christmas period and hopefully we can keep it going."
Liverpool's last trophy was the 2012 League Cup and the former Manchester City midfielder said he was optimistic the club, who are sixth in the Premier League, could end their wait for silverware.
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"It is a talented squad of players, we have a great mix of youth and experience and obviously a new manager. It is exciting times for everyone," Milner said.
"If we keep working hard, keep improving, keep doing our job then hopefully we can be successful. We just want to keep getting the wins on the board.
"Hopefully get into January and February and still be in all the cup competitions and give ourselves a shot in one of the cups."
(Reporting by Shravanth Vijayakumar in Bengaluru. Editing by Patrick Johnston)
