Ever since talk of a big-money move for the Germany international first surfaced in 2020, Anfield has been billed as his most likely destination.
Werner has left a door open for the Reds to make a move, while many have talked up the value of Jurgen Klopp adding a fellow countryman to his ranks on Merseyside.
Rival interest is, however, expected to be shown if the prolific 24-year-old becomes available on the open market.
Burley believes Frank Lampard should be looking to join the chase for Werner as he would be a useful addition to the attacking armoury at Stamford Bridge.
The Blues could also offer the highly-rated frontman more guarantees when it comes to game time in west London, with it possible that the presence of Sadio Mane, Mohamed Salah and Roberto Firmino at Liverpool could work against them.
Former Chelsea midfielder Burley told ESPN FC: "You want to back yourself as a player.
"You've got a manager in Klopp who will be very enthusiastic in trying to sell the platform to him.
"Clearly when I played, you played on the Saturday, you played on a Wednesday and expect to play the following Saturday if you played well enough. If you got told you were left out of the side, you knew it wasn't for resting purposes, it was because you were dropped.
"The game has changed, you've got to have a deep squad and a quality squad.
"I think Klopp can sell to Timo Werner that Sadio Mane, Roberto Firmino and Mohamed Salah have carried the load for Liverpool, and they're not going to play 50 or 60 games per year.
"I'm not surprised Chelsea would be interested, though, he ticks every box for them.
"He can play out wide, they've got wide players, he can play through the middle, he works hard, he presses when he's not got the ball, it absolutely makes sense for him."
Plenty have warned Werner that he may have to make peace with bench duty, initially at least, if he were to head for Anfield.
There is, however, talk of Mane or Salah moving on in the not too distant future and that would open up a prominent role in Klopp’s plans.