The German international has already scored eight goals in just 13 games for RB Leipzig this season.
Werner's impressive form has prompted Liverpool to up their efforts to secure a deal for him.
Furthermore, according to transfer expert Ian McGarry (via the Daily Star), Werner is said to be keen on the move to Anfield.
McGarry believes, however, that a summer move may be more likely than one in the winter transfer window.
“Timo Werner is a target for Manchester United and Liverpool in the January window but it may be the summer before he actually makes the move,” McGarry said on Reach Plc’s Transfer Window podcast.
“Raphael [Honigstein] told us that it was widely believed the player has a recision clause in his contract but no-one as of yet knows what it is.
“What we can tell you on the transfer window today is that Liverpool have begun the process of formal negotiations with RB Leipzig for the player’s transfer.
“We understand that contact has been made and indeed is ongoing between Liverpool and the German Bundesliga side and that Werner himself is keen for a move to Anfield.
“Of course, he would link up with countryman Jurgen Klopp.”
Liverpool are understood to want to freshen up their options in attack, despite having an existing front three of Sadio Mane, Mohamed Salah and Roberto Firmino.
United, on the other hand, have made it clear they are actively looking to add firepower to their ranks.
Marcus Rashford and Anthony Martial may be returning to goalscoring ways, but it is reportedly the Red Devil's belief that they shouldn't be relied upon.
United are thought to see Juventus' Croatian striker Mario Mandzukic as another option.
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