The Spain international, who joined the Bundesliga champions from Barcelona back in 2013, has informed Bayern that he will not sign a new contract.
The 29-year-old has only a year left to run on his current deal and is expected to depart the Allianz Arena for a cut-price fee, with Liverpool strongly linked with the playmaker.
Jurgen Klopp has been cautious in his assertions about adding to his squad this summer despite allowing Dejan Lovren and Adam Lallana to head for the exit.
But Barnes thinks that while Thiago would bring a different dynamic to the Merseyside club, he may not be able to play on regular basis due to stiff competition for places in midfield.
"I don’t think he will come and be a first-team regular, I think Liverpool know what their best [starting] 11 is and they were 20 points ahead of everybody else, so they won’t need to change that," he said.
"But in certain games, when teams play differently, Klopp may feel that a player like him might make a difference in certain games instead of changing the way Liverpool will play and put him ahead of one of the players, who are all very similar.
"Fabinho is the real holding midfield player that will be the first name of the midfield three, Thiago may come and add to the other two positions."