The former Barcelona midfielder controlled the game as Spain rallied to secure a late draw against Germany on Thursday, having also impressed in the Champions League final win over PSG for Bayern.
Although he was linked to Liverpool for months, their failure to make a move has alerted their bitter rivals ahead of the new season, and Thiago has since been asked about his preference.
“I only think about the game against Ukraine. Afterwards, we will see,” said Thiago.
“Bayern is my home and I am happy to be there.”
The latest comments of the midfielder suggest that he could end up staying at the club beyond the summer, which is a twist on a statement made by Bayern CEO Karl-Heinz Rummenigge.
He said at the end of August: "We are expecting an offer from another club in the next few days. He told us that at the end of his career, he would like to try something new."
With Thiago available for a fee of around £30m, some Liverpool supporters have been confused by the lack of action taken by the club in the transfer market.
Jurgen Klopp has insisted in recent months that the club is currently financially limited, which has already seen them miss out on Germany striker Timo Werner.
When asked by Servus TV about Thiago, Klopp said: “There are a lot of interesting players out there but if someone is interesting for us I can’t say right now.
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“Due to COVID-19 you have to think five times about what you can and what you can’t do. We always have to pay attention to the financial aspect. We don’t know how much money will come in.
“Nobody knows but it seems like some other teams have a more positive outlook on the future… if you look at Chelsea for example [laughs].
“But I am very happy with my team right now. If something transfer related will happen we have to see.”