In comments published by UAE daily Gulf News on Thursday, Bu Amim added: "We are with you in this difficult time and respect your request for family privacy. As and when you decide to return to the circuit, you can always count on us. We will be more than delighted to welcome you to Dubai. Consider Dubai your second home."
Woods missed last year's Desert Classic due to a knee injury but Bu Amim said he was hoping Woods will return to play in future editions of the tournament, if not in 2010.
"We would love to see him playing in our event, but at the same time, we do realise his number one priority at this time is his family," Bu Amim told the paper.
"Having the world's greatest golfer player in your field is something many tournament organisers dream of; so for us to be able to welcome him to Dubai for the fifth time in eight years was a major boost for golf in the Middle East, especially Dubai."
The 2010 Dubai Desert Classic will be held at the Emirates Golf Club from February 2-7.