The 24-year-old forward has been strongly linked to a move to England, the attacker said to be supportive of Anfield.
Manchester United and Chelsea have also been linked to Werner, his contract with RB Leipzig expiring in 2023.
Werner had his best scoring season to date, scoring 24 goals, including a hat-trick against Mainz on Sunday.
While a move to Liverpool seems logical given the German connection with Jurgen Klopp, Hargreaves thinks Werner would be better suited to Old Trafford as there is no guarantee of starting at Anfield.
“Well, he will not overtake Bobby Firmino, who is one of my favorite players to watch,” said Hargreaves in a comment on BT Sport.
“I think that’s the thing. Wherever he goes, he has to play. With the way (Manchester) United currently plays, I could see it there. They need a number nine. “
“Chelsea could be a good fit, I just think it is perfect for Liverpool somehow, but it is not guaranteed to start. If he’s happy to be in the top three, then yes, he would be perfect for Jurgen Klopp.
“He works hard, he’s a good goalscorer, he’s a good teammate, all these things he needs but he’s not going to play in front of Roberto Firmino, I don’t see that. He’s too good in this team. “
However, Hargreaves added to his belief that Werner would suit Liverpool’s playing style and believes his explosive nature would make him a great fit, comparing the striker to Fernando Torres.
He said: “I think Timo Werner is going to score goals wherever he goes, but I think his decision will depend on the staff.
“Timo will now do his homework on who will be perfect for his game.
“We saw him with Fernando Torres when he left Liverpool. The way they played – an incredibly defensive team with Stevie Gerrard playing those balls in the middle.
“It was a match made in heaven. Then Torres went to Chelsea, a team that had a lot of slow possession and there was no room for him.
“In the end, it is not a good choice. Fernando was a great player and Chelsea were a great team – but you have to play on a player’s strengths.
“I think Timo Werner is that guy, the Fernando Torres guy, where he’s super explosive. He will run away from anyone.
“Having this ability to run behind and in this space would suit his game – and Liverpool can do it.
“They counter and transition better than anyone. It would suit Liverpool. ”