"I am aware of the interest from Japan but... we have a lot of games coming up and they have, absolutely, first priority at the moment," the Dane told Kyodo News on Wednesday.
"When the season finishes in May, I will think about my future. It could be here in Lekhwiya or somewhere else."
Laudrup played briefly with Japanese club Vissel Kobe at the end of a glittering career which included league titles with Barcelona, Real Madrid, Juventus and Ajax Amsterdam.
The JFA have said they would like Javier Aguirre's successor in place by March 7 so the new manager can take in the start of the J-League season and be fully up to speed before the World Cup qualifying campaign gets underway in June.
The JFA said previously the manager would be foreign and picked from a shortlist of five after sacking Mexican Aguirre early this month because of fears his alleged involvement in a match-fixing case in Spain could hurt the team.
But the JFA have also not ruled out appointing a caretaker boss for the friendlies against Tunisia and Uzbekistan at the end of March.
Laudrup signed a one-year deal to coach Lekhwiya in July -- the latest stop on a nomadic managerial career which has taken him to Spain, Russia and England.
Lekhwiya are one point behind leaders Al Sadd with seven matches remaining in the Stars League. They also begin their AFC Champions League Group A campaign next week side away to Iran's Persepolis.
(Wrting by Patrick Johnston in Singapore; editing by Sudipto Ganguly)
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