Gerrard's expected move to MLS Cup winners Galaxy was confirmed on Wednesday, with the midfielder - who turns 35 in May - set to join when his Liverpool contract expires.
Several players have opted to make temporary switches to clubs in Europe from MLS teams in the past, with former Galaxy star David Beckham having enjoyed two spells at Milan and ex-New York Red Bulls striker Thierry Henry having returned to Arsenal in 2012 for a four-game stint.
The issue has sparked debate recently after Frank Lampard delayed his move to new MLS franchise New York City FC to extend his loan deal at Manchester City until the end of the season.
Klein, though, insists Gerrard's sole focus after leaving Anfield will be on helping to bring more success to Galaxy.
"His focus right now is finishing the season with Liverpool and in the summer he will come and focus on his time with LA Galaxy," Klein told BBC Sport.
"One of the things that was important for us to hear from Steven was the decision came down to continuing his career in a very good way and with a club that wanted to continue to win.
"We are quite confident in the environment we provide for this next step of his career."
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