Gallacher, 18, underwent a week-long trial at the Reds' Kirkby Academy earlier this month and impressed sufficiently to earn a permanent transfer to Anfield.
Inter Milan will sign Daniel Sturridge on loan until the end of the season before making the deal permanent in the summer.
Liverpool are keeping close tabs on one or two players but no decision has been made whether the deal will be completed in January or in the summer.
Daniel Sturridge is keen to leave Liverpool with Inter Milan and Sevilla interested in signing the England international.
Sturridge has not featured for the Reds for seven weeks and is widely expected to leave Anfield before the close of the transfer window.
Lallana has endured an injury-riddled season so far, starting just one Premier League match all season.
Emre Can's current deal at Liverpool will expire after the end of the ongoing season. He is a transfer target for Serie A winners Juventus.
Daniel Sturridge is keen to leave Liverpool in January with Inter Milan favourites to sign the striker. Danny Ings' desire for a move away is likely to be blocked.
Reports suggest that Russian giants Spartak Moscow are keen to sign Serbian winger Lazar Markovic, who has not played a competitive match for Liverpool since May 2015.
Reports had suggested that the Reds had begun discussions with Gremio for their prized attacker, who has been linked with a move to England in recent months.
Thomas Lemar has been attracting interest from Arsenal and Liverpool, while Barcelona are also believed to be interested in securing his services.
Swansea City ended Liverpool's 18-game unbeaten run in all competitions at the Liberty Stadium on 22 January.
Redknapp feels Reds have been strengthened by the arrival of Dutch centre-back Virgil van Dijk from Southampton.
Nuri Sahin moved to Real Madrid in 2011 and rejoined Borussia Dortmund 18 months later on loan. In 2014, his transfer was made permenent.
Jurgen Klopp says Liverpool are not actively looking for potential new targets that they "don't know so far", but admits he could do more business if a deal really stands out.
Inter Milan are keen to sign Daniel Sturridge during the ongoing January transfer window as Luciano Spalletti wants a proven goal scorer.
Liverpool could hand returns to Virgil van Dijk, Jordan Henderson and Alberto Moreno for the visit to Swansea City on Monday after the trio all returned to training.
Following the departure of Philippe Coutinho to Barcelona, reports claim that Liverpool are no longer willing to sanction a loan exit for teenager Ben Woodburn.
La Liga side had offered to take Sturridge on loan for the rest of the season, but were turned down by Liverpool technical director Michael Edwards.
Cardiff City have signed Liverpool midfielder Marko Grujic on loan until the end of the season.
Serie A leaders are in the market for a goalkeeper to replace Pepe Reina, whose contract expires in the summer.
Liverpool goalkeeper Simon Mignolet is considering his options having been replaced by Loris Karius as Jurgen Klopp's first-choice stopper in the Premier League.
