"Landon is a player who bring all sorts of qualities, he has developed into one of the top players in North America and Mexico," said Klinsmann, who was a technical advisor at Galaxy before he took over as Bayern coach on July 1.
On Tuesday, Donovan was named US football's Player of the Year for the fifth time, the same day he started a ten-day trial with Bayern while his United States club Galaxy are on their annual winter break.
Having struggled to impress on his last sojourn to the Bundesliga when he had a brief spell at Bayer Leverkusen, Donovan said he is enjoying his time in Munich and is keen to stay.
"As a person and a player, I am completely different now to how I was then, I have matured. I am ready," said the attacking midfielder who played in Bayern's 6-1 win over their second team on Wednesday. "I believe I can keep up with all the other players, even if I am not the best player here."
Having struggled to make the grade in Germany last time, Donovan admits he has learned from the experience.
"I recognise Leverkusen wasn't the problem, I was," he said. "I just wasn't ready for it."
And Bayern manager Uli Hoeneß has been impressed with what he has seen so far. "What he has shown so far is okay, he can certainly kick," said Hoeneß.
A decision on whether Donovan becomes a permanent Bayern player will be taken at the end of next week, added Hoeneß.
Donovan has a contract with Galaxy which runs until 2012 and with 105-caps to his name, his market value is around €2.5 million ($3.1 million).
Just like Galaxy's other star, former England captain David Beckham who will join AC Milan for three months later this winter, Donovan may also sign only a short-term contract with Bayern.
But he ruled out any comparisons with Beckham. "I am not a good-looking posterboy, I am a footballer," was his curt reply.
Donovan has an impressive CV. He was the top-scorer in Major League Soccer last season with a career-high 20 goals in 25 matches, although the Galaxy failed to qualify for the eight-team MLS playoffs. And the 26-year-old is the top scorer leader for the United States with a total of 37 goals in 105 international appearances.
His 2008 Player of the Year award, voted on by the US media, was his fifth and he is the only player to earn the accolade more than twice.