The 20-year-old is thought to have rejected a new deal worth £100,000-a-week as he wants parity with the club's top earner Daniel Sturridge.
Sterling has two years left to run on his current deal, and he revealed his frustration in an interview with BBC when he said: "If, at that point in time, I was offered a contract, I most definitely would have signed straight away, probably for far less money than being said now.
"I just think the timing was a bit off."
GETTY
Raheem Sterling is yet to sign a new deal with Liverpool
But he plays at Chelsea. This could be very expensive for Bayern
Franck Ribery
Franck Ribery claims Chelsea's Eden Hazard would be a more logical choice as a long-term replacement for him or Arjen Robben at Bayern Munich.
Wolfsburg's Kevin De Bruyne has been talked up as a possible Bayern target, but Ribery believes Hazard would be a better signing and told German paper Sport Bild as quoted by ESPN: "Hazard attacks all of the time. He loves to run at his opponent.
"But he plays at Chelsea. This could be very expensive for Bayern."
Hummels hit back at claims he promised to join the Red Devils when Sir Alex Ferguson was in charge.
And Dortmund director Michael Zorc insists Hummels won't be sold anytime soon and told Sport Bild: "Like Marco Reus [who signed a contract through to 2019 in February], Mats shapes our team and that should not change for as long as possible."
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