The Togo international was granted a leave of absence on Wednesday with Tottenham releasing a statement saying the striker was allowed to return home for "personal reasons", with reports suggesting a family member has been taken ill.
It is not known how much action the 30-year-old will miss, but he definitely sits out Thursday's UEFA Europa League tie with Besiktas and is unlikely to return in time to face Swansea City in the Premier League on Sunday.
And Pochettino will not rush the former Manchester City man back to White Hart Lane.
"I hope he sorts his problems. I don't know how long [he will be out] but we hope he will stay with us next week to train," he said.
"When you have a problem, your mind is not quite [right]. It is difficult to give your best.
"I have always told you that players are human. Family is important. They need to fix when family matters happen. You need to sort it. If not, it is difficult to give the best.
"It is important that he takes time, sorts out the problem and when he is back is ready to train and available."
Adebayor has fallen down the pecking order behind Harry Kane and Roberto Soldado in recent weeks after scoring just two goals in 12 appearances across all competitions this season.
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