The former Bayern Munich and Germany captain believes the World Cup-winner was right to reject a move to Anfield.
Gotze had been widely linked with a move to Anfield to reunite with his former Borussia Dortmund manger Jurgen Klopp in recent weeks, and it was looking likely at one stage that a deal may be struck.
However, the 23-year-old midfielder, who scored the winning goal for Germany in the World Cup final two years ago, confirmed earlier this week that he wanted to stay at Bayern Munich and play under incoming manager Carlo Ancelotti.
Matthaus believes the Bayern star was right to reject a reunion with Klopp and instead fight for his place in Munich because the Reds cannot offer Champions League football, and praised the midfielder for not taking the "easy solution".
The former star told TZ: "I don't know whether there was indeed an offer from Liverpool. But why would he join a club that do not even play in the Champions League? He would have taken the easy solution with a move to Liverpool. But the easy solution is not always the right solution.
"Mario has shown with his latest comments that he is ready to fight for his place. I applaud his decision to stay put. He is not taking the easy way out, but is taking on the challenge. He wants to show Bayern what he can do."
Gotze's apparent decision will have come as a huge blow to Klopp and Liverpool fans as the club look for a marquee summer signing to help convert them from a top-eight side to top-four and possible even title contenders next season.