TFG said earlier on Friday it was open to selling a controlling stake as part of efforts to attract fresh investment, less than two years after it acquired Everton from former owner Farhad Moshiri in December 2024.
"I truly believed with new ownership we were in it completely," Moyes told reporters ahead of Everton's Premier League game at Hull City on Sunday.
"My ambition coming back was trying to get Everton back to the levels they have been in the past and that is challenging for Europe more often.
"It has been a difficult summer for us. I only found out this morning. Maybe I am a little bit surprised, but maybe I shouldn't be that surprised."
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Everton are seventh in the table after five games.
TFG took control of a club grappling with financial difficulties and a prolonged period of instability and has since overseen Everton's move into the Hill Dickinson Stadium while working to improve their financial position.
"When TFG became custodians of Everton, the club faced significant financial uncertainty and challenges both on and off the pitch," the owners said in a statement.
The group said its immediate priority had been to provide the stability, investment and support required to secure Everton's future, including completing the new stadium.
"With that foundation now safely in place, the time is right to consider the next chapter for Everton," TFG said.
TFG added that it would only consider proposals from parties it believed could build on the progress made since its takeover and added that it would continue to support the club on and off the pitch throughout the process.
TFG's decision follows a transfer window that, according to British media, drew criticism from supporters. Everton generated significant income through player sales but made only limited additions to their squad before the deadline.
TFG, which also owns Italian club AS Roma and French side AS Cannes, said it had retained investment bank Moelis & Company to advise on the process.
The group and Everton said they would make no further comment while the process was under way.