Thiago has been heavily linked with a switch to Anfield with the Premier League champions keen on the Spaniard.
United are also believed to be eager as Ole Gunnar Solskjaer attempts to strengthen his side this summer.
Though reports from Norway suggest that, while there has been communication over a move, Thiago’s wage demands are too high.
Thiago is available for just €30m this summer having played a key role in Bayern’s treble-winning season.
Bayern Munich CEO Karl-Heinz Rummenigge has confirmed that Thiago is likely to depart the Champions League winners this summer.
He said: “It looks like he will leave us. It was important for him that he showed that he can play well in the big games. When it comes to that, it’s a finish that hurts a bit.
“I expect an offer for him in the next few days.”
Former Bayern and Manchester United star Owen Hargreaves believes Thiago would fit in at any of the Premier League giants.
“They (Liverpool) don’t have him (a player like him). On his day, he’s one of the top five midfielders in the world," Hargreaves said.
“I think everybody needs him. Man United, Arsenal, anybody would take him.
"He’s one of those players, if you played with him, you’d be blown away by how good he is.
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"The only issue he’s had is injuries. He’s had big injuries at Bayern.”
United are yet to make a signing during the transfer window though are believed to be close to sealing a deal for Ajax star Donny Van de Beek.
Liverpool, meanwhile, have brought in Kostas Tsimikas though Jurgen Klopp is not expected to be too busy in the market.