Reports suggested that Liverpool were keeping tabs on the player during the summer, when the club required an overhaul in midfield, following the departures of Jordan Henderson and Fabinho.
After starting the season very short on numbers, Jurgen Klopp was eventually able to welcome the likes of Dominik Szoboszlai, Ryan Gravenberch and Wataru Endo to the club to fill the gaps in the squad.
Alexis Mac Allister was an earlier arrival, but along with Szoboszlai, the two have had injury issues for parts of the season so far.
Gravenberch has also struggled to make much of an impact on Merseyside, with homegrown Curtis Jones now the preferred option in midfield.
Klopp could also be without Endo for an extended period, given he is away on international duty at the Asian Cup with favourites Japan.
Therefore, Calciomercato claim that Liverpool are in the race for Shakhtar's Sudakov, but there is plenty of competition for his signature.
Valued at €40m (£34m) by his club, Sudakov is also believed to be of interest to Juventus and Napoli this month.
Following the lengthy suspensions handed out to Paul Pogba and Nicolo Fagioli, midfield is likely to be the area where Juve will strengthen this month, as they attempt to hunt down Inter Milan at the top of Serie A.
Scudetto holders Napoli are a long way off the pace at the top though, and have a fight on their hands just to finish in the top four, and could seek reinforcements in that position too, especially after selling Elif Elmas to RB Leipzig.
Sudakov's star has risen in recent months thanks to his performances in the Champions League, with Barcelona, Bayern Munich and Manchester City also believed to be interested in the player.
The 21-year-old is a key player for his national side Ukraine, and he could play a major role in their upcoming Euro 2024 playoff against Bosnia-Herzegovina.
After being at fault for a goal in their 2-1 defeat away to Italy, the youngster may well be determined to put on an inspirational performance to lead his nation to another major tournament when those playoffs come around in May.