Speaking on ESPN at halftime of the Galaxy's 5-2 loss to the Portland Timbers on Wednesday night, Te Kloese dismissed reports that Mexico's all-time leading scorer may be headed back to his boyhood club in Guadalajara.
"It's been a challenging year for everybody and certainly for Javier," Te Kloese said. "He came in with high expectations ... we haven't been able to connect the high expectations so far and there's no truth in any rumors about him going to Chivas, or anything else."
He ruled himself out of Wednesday's game due to an undisclosed injury prior to the Galaxy officially listing him as not available for the match in Portland.
The defeat to the Timbers saw the Galaxy remain in last place in MLS' Western Conference, having won only three points over the last nine games.
Te Kloese also said brushed off talks about Galaxy manager Guillermo Barros Schelotto's future amid the club's poor run of form. In recent weeks, Barros Schelotto's position is speculated to be unstable, with Robbie Keane and Javier Aguirre linked with the job, but Te Kloese said is not the time to discuss the manager's job.
"I think it's a challenging moment to discuss it right now," Te Kloese added, with the Galaxy already 3-0 down. "I think beyond even the manager's position, the players, my decision, my part is being first of all held responsible.
"We have to take responsibility and evaluate as best we can, obviously, after a very rough season so far and I think it's not the time to discuss anything on the manager's position or anybody within the organization before we sit together and evaluate."
Following the game, Schelotto spent less than a minute at the post-match news conference.
The former Boca Juniors manager said: "The first half we committed a lot of defensive errors, it's not necessary to talk about them.
"We could spend a lot of time talking about what happened in the first half, the reaction in the second, of how close we were to narrow the margin at 3-1, but the result is definitive.
"There are three games left over the next 10 days and we have to focus on winning them. We have the possibility of making the playoffs, depending on other results, and we'll work towards winning and have the chance to qualify. I thank you and hope you understand the moment. Good night."