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Rival interest has, however, fallen away, leaving the path clear for Frank Lampard and Chelsea to swoop in.
They are yet to get Werner tied a contract, but appear to have emerged victorious in a keenly-contested race.
Hargreaves is surprised that United did not seek to pip a Premier League rival to a prolific striker who could prove decisive in future title challenges.
The former Red Devils midfielder, who keeps a close eye on the Bundesliga having spent time with Bayern Munich in his playing days, told BT Sport of Werner: "Well I think he's perfect, I think he could have been perfect for Man United as well but I think it's brilliant for Frank Lampard and Chelsea.
"A proven goalscorer but the curious thing for me is how he fits in with Tammy Abraham, because I love Tammy's game and I think he's been tremendous.
"So maybe Timo Werner can play off the left side at times but they have multiple players there for those positions, with [Callum] Hudson-Odoi and [Christian] Pulisic.
"But it's a terrific signing for Chelsea, I think they needed to make a statement and they've done that.
"To go with [Hakim] Ziyech and all these terrific young players, I think Chelsea are building something, not to compete next season for the Premier League but definitely in two or three years' time to compete to win the Premier League.
"Terrific signing, I think Chelsea fans are going to love him."
United, who have agreed an extension to Odion Ighalo's loan through to January 2021, appear to be focusing their attention away from the striking department at present.
Ole Gunnar Solskjaer is more concerned with adding greater creativity to his ranks than further firepower, with the likes of Borussia Dortmund winger Jadon Sancho and Aston Villa playmaker Jack Grealish topping his wish list.